President Biden is set to nominate Federal Reserve Chairman Jerome Powell to a second term leading the central bank, the White House said Monday, opting for continuity in U.S. economic policy despite pushback from some Democrats who wanted someone tougher on bank regulations and climate change.

Mr. Biden will also nominate Fed governor Lael Brainard as vice chair of the central bank’s board of governors, the White House said.

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President Biden is set to nominate Federal Reserve Chairman Jerome Powell to a second term leading the central bank, the White House said Monday, opting for continuity in U.S. economic policy despite pushback from some Democrats who wanted someone tougher on bank regulations and climate change.

Mr. Biden will also nominate Fed governor Lael Brainard as vice chair of the central bank’s board of governors, the White House said.

Mr. Biden’s decision ends months of guesswork in financial markets and Washington policy circles over one of the world’s most important economic policy posts. Mr. Powell is expected to win bipartisan Senate confirmation; of the 84 lawmakers who voted for him four years ago, 68 of them are still in office, equally split between the two party caucuses.

The Fed chairman met with the president on Nov. 4. The president also interviewed Ms. Brainard on the same day.

Mr. Biden spoke with Mr. Powell and Ms. Brainard on Friday to inform them of his decision, according to a person familiar with the matter.

Mr. Biden can put his stamp on the central bank with three additional appointments. There is already one vacancy on the Fed’s seven-member board of governors, and Fed Vice Chairman Richard Clarida’s term as governor will expire in January. The four-year term of the vice chair of bank supervision, previously held by current Fed governor Randal Quarles, expired in October and he plans to retire around the end of the year. Mr. Biden will announce those appointments in early December, the White House said Monday.

Fed governor Lael Brainard will be nominated to serve as vice chair of the central bank’s board of governors, the White House said.

Photo: Al Drago/Bloomberg News

“If we want to continue to build on the economic success of this year we need stability and independence at the Federal Reserve—and I have full confidence after their trial by fire over the last 20 months that Chair Powell and Dr. Brainard will provide the strong leadership our country needs,” Mr. Biden said in a statement on Monday.

Mr. Powell faces an especially delicate path now as the recovery from the Covid-19 pandemic and the government’s response has sharply boosted demand and disrupted global supply chains, sending inflation to its highest levels in more than a decade.

The danger for the Fed is twofold: Officials don’t want to overreact by raising interest rates and cooling down the economy if supply-chain bottlenecks repair themselves over time. But they also don’t want to underreact as wages rise, fueling a more traditional inflationary cycle.

Mr. Powell, 68 years old, is seen by supporters inside the administration and in markets as a steady hand whose extensive, personal outreach helped restore bipartisan support for the central bank one decade after its reputation was badly bruised by the 2008 financial crisis. Mr. Powell, a Republican and former private-equity executive, was named to the Fed’s seven-member board 10 years ago by then-President Barack Obama and elevated to the chairman’s post four years ago by then-President Donald Trump.

Mr. Powell was backed for the job by several members of Mr. Biden’s economic team, including Treasury Secretary Janet Yellen, who served as Fed chairwoman from 2014 to 2018.

The political support Mr. Powell cultivated proved valuable throughout his term as chairman—first, when he faced steady attacks in 2018 and 2019 from Mr. Trump for raising interest rates, and later, when he led a rapid, aggressive response to douse a global financial panic triggered by the coronavirus pandemic in March 2020.

Under Mr. Powell, the Fed orchestrated one of the largest and boldest economic policy responses since World War II, acting in concert with Congress and the U.S. Treasury. The Fed slashed interest rates to zero and then purchased trillions of dollars of government debt and offered to buy trillions more in loans and other assets to backstop credit markets.

Mr. Powell unveiled in 2020 a substantial shift in the way the central bank conducts interest-rate policy when he announced the Fed would set aside its practice of raising rates to pre-empt inflationary pressures and instead leave rates lower for longer to spur a faster recovery following downturns.

The shift reflected the Fed’s reassessment of the economy in 2019, when inflation didn’t pick up as policy makers expected it would with the unemployment rate falling to its lowest levels in 50 years. Mr. Powell navigated a policy U-turn from raising rates to cutting them while facing sustained criticism from Mr. Trump, who privately and publicly threatened to sack the Fed leader for not providing easier monetary policy.

At the beginning of this year, Fed officials were anxious to avoid a rerun of what followed the 2007-09 recession, in which weak growth forced the central bank to deploy novel measures to stimulate an economy in which short-term rates were already pinned near zero. But the reopening of the economy and a $1.9 trillion federal spending boost signed by Mr. Biden in March, on top of trillions of relief spending in 2020, fueled a larger-than-anticipated surge in consumer prices, which rose 4.4% in September from a year earlier, according to the Fed’s preferred gauge.

From the Archives

Federal Reserve Chairman Jerome Powell described the outlook for inflation in the U.S. economy and said there are signs that prices that have moved up quickly should cease rising and retreat. Credit: Al Drago/Associated Press The Wall Street Journal Interactive Edition

The Fed recently began shrinking its $120-billion-a-month bond-purchase stimulus program by $15 billion every month, a pace that could end the purchases around June. After that, the focus will turn to when and how quickly the central bank should raise interest rates from near zero.

Mr. Powell has to manage a group of 12 reserve bank presidents and up to six other governors who participate in rate-setting meetings. Several are growing more concerned that high inflation will persist, requiring the central bank to raise rates sooner or more aggressively than expected just a few months ago. Others are nervous about overreacting and have argued that pre-pandemic dynamics in which inflation, interest rates and global growth were historically low will eventually reassert themselves.

Mr. Biden’s political fortunes in the coming years may be tied to how Mr. Powell responds. If the Fed waits too long, Americans could face higher inflation for years or the central bank could be forced to raise rates aggressively, convulsing financial markets and putting the economy into a downturn. If it moves too fast or too soon, it risks prematurely slowing down hiring.

Mr. Powell has argued that price pressures reflect bottlenecks from disrupted supply chains, temporary shortages and a rebound in travel. But he has warned in recent weeks that price pressures could also reflect stronger demand and that overwhelmed supply chains could lead to more persistent inflation than officials initially anticipated.

“We have to be in a position to address that risk,” he said at a Nov. 3 press conference. “We think we can be patient. If a response is called for, we will not hesitate.”

In recent months, a range of current and former Democratic lawmakers along with progressive economists had spoken out in favor of extending a second term to Mr. Powell. They argued his skill transcending the polarization that has gridlocked much of Washington made him uniquely positioned to provide political support and intellectual backing for progressive policies that could elude even the most qualified Democrats.

“In this political environment, any other nominee would risk being perceived as a political choice,” said Roberto Perli, an analyst at Cornerstone Macro, a research firm in Washington. Mr. Powell had steered monetary policy in a direction “that is very much in line with the priorities of this administration, but he did so for sound economic reasons, not political reasons,” said Mr. Perli, a former Fed economist.

Mr. Powell navigated attacks from both Mr. Trump and Sen. Elizabeth Warren (D., Mass.) in “a high-wire act of political survival,” said Marc Sumerlin of economic-consulting Evenflow Macro. If the Fed raises interest rates to slow down the economy next year, “Biden may come to feel the same way as Trump, but the nation will be better served with continuity,” he said.

Treasury Secretary Janet Yellen, who served as Fed chairwoman from 2014 to 2018, had backed Mr. Powell for the job.

Photo: michael reynolds/Shutterstock

Mr. Powell’s leadership of the Fed faced new scrutiny in recent weeks because of financial disclosures by senior central bank officials that revealed extensive trading last year, when the Fed deployed unusual countermeasures against the pandemic.

The reputational crisis prompted two Fed reserve bank presidents to retire early. Mr. Powell announced in October a sweeping revamp of policies on how its leaders manage personal investments to minimize even the appearance of conflicts of interest.

A vocal minority of progressive groups pressed Mr. Biden to replace Mr. Powell with someone more committed to aggressive bank regulation and to using the central bank’s supervisory powers to address climate change. Some of them favored Ms. Brainard, an economist named to the board by Mr. Obama in 2014. She supported Mr. Powell’s monetary policy decisions while dissenting on moves to ease certain banking regulations.

Ms. Warren told Mr. Powell at a Sept. 28 hearing that she would oppose his nomination because of the Fed’s record of reducing regulations on banks in recent years. “That makes you a dangerous man to head up the Fed,” she said. Later, she cited the questionable trading activities by Fed insiders as a sign of failed leadership by Mr. Powell.

Other Democrats expressed concern that progressives’ priorities might further yoke the Fed to broader partisan warfare that the institution has largely avoided. They worried such moves could undermine its effectiveness on a new monetary policy strategy that has placed new emphasis on tighter labor markets.

“It makes me very, very uneasy if we’re going to appoint somebody…to move the Fed and lose its independence,” said Montana Sen. Jon Tester, a moderate Democrat who in September strongly backed Mr. Powell’s appointment.

Elevating Ms. Brainard to vice chair represents a compromise of sorts between the two camps. The vice chair of the board, together with the New York Fed president, traditionally serve as the Fed chair’s top lieutenants in designing monetary policy. Ms. Brainard could take over as vice chair next February.

Ms. Brainard has been strongly supportive of the Fed’s policy shift during Mr. Powell’s tenure and has generally advocated for delaying interest rate increases to avoid the risks of inflation being stuck below the central bank’s 2% target.

Mr. Biden’s team had been in regular contact with senators and their staff in recent weeks to get their input, according to a person familiar with the process. He met at the White House with Ms. Warren on Nov. 9 to discuss the matter, and the president and his staff regularly briefed Senate Banking Committee Chairman Sherrod Brown (D., Ohio), the person said.

Mr. Powell has scheduled hundreds of meetings with lawmakers during his four years in office, and he remains well liked by politicians on both sides of the aisle. Rep. Emanuel Cleaver (D., Mo.) recalled inviting Mr. Powell to his district several years ago and introducing him to a cross section of rural Missourians and Kansas City residents.

“There was no exception—everybody thought, ‘Hey, this guy is OK. He’s a straight-shooter.’ There’s nothing partisan about his presentation,” said Mr. Cleaver.

Mr. Powell drew on that political capital after the pandemic hit in 2020 to urge lawmakers to spend more money. “This is the time to use the great fiscal power of the United States to do what we can to support the economy and try to get through this with as little damage…as possible,” he said in April 2020.

By that point, the Fed had already slashed rates to zero and was buying massive quantities of debt to stave off a financial meltdown. It also had unveiled lending backstops to businesses, cities and states that went far beyond anything the Fed had done during the 2008 financial crisis.

The unemployment rate, which stood at a half-century low of 3.5% in February 2020, soared in April 2020 to 14.8%, the highest level since the 1930s, as the economy was placed into the equivalent of a medically induced coma to restrain the spread of Covid-19. Unemployment steadily dropped, falling to 4.6% in October.

The Fed’s response earned accolades from lawmakers—a contrast with the unpopular bank bailouts it arranged in 2008. “We all remember well spring of 2020, when the world economy almost melted down, and it didn’t in substantial part because of the actions that you and your colleagues took,” said Sen. John Kennedy (R., La.) in a July hearing. “You kept this thing in the middle of the road. Now, some days you had to do it with spit and happy thoughts, but you kept it in the middle of the road.”

Write to Nick Timiraos at nick.timiraos@wsj.com and Andrew Restuccia at andrew.restuccia@wsj.com