Glencore PLC said Tuesday that it would pay at least $1.2 billion and that two business units would plead guilty to bribery in the U.K. and to conspiracy to violate U.S. anticorruption laws, resolving criminal probes that have hung over the global mining and trading business for years.

The long-awaited guilty pleas and fines, covering a range of misdeeds including market manipulation and bribery, are related to Glencore’s past commercial conduct in the developing countries where it and other trading powerhouses obtain minerals and other resources and ferry them around the world.

Glencore International AG will pay about $700 million to resolve a U.S. Justice Department foreign-bribery investigation and $39.6 million to settle bribery claims in Brazil, according to the company. Another unit has agreed to pay $485 million to settle U.S. criminal and civil investigations into manipulation of fuel-oil prices, Glencore said.

Britain’s Serious Fraud Office charged another unit, Glencore Energy UK Ltd., with seven counts of bribery in connection to payments of $24 million for preferential access to oil in Africa.

As part of its settlement of the U.S. investigations, Glencore International pleaded guilty to one count of conspiracy to violate the Foreign Corrupt Practices Act, the company said.

In the separate criminal market-manipulation case, another unit, Glencore Ltd., pleaded guilty to one count of conspiracy to rig commodity prices.

The Brazil fine stems from Glencore’s part in a corruption probe known as Operation Car Wash, which involved payments related to state-controlled Petróleo Brasileiro SA, or Petrobras.

Corporate penalties greater than $1 billion are relatively rare but not unprecedented in cases that involve overseas misconduct and law enforcement from different countries. One of Allianz SE’s U.S. investing divisions agreed this month to pay about $6 billion in penalties and restitution to resolve a federal securities-fraud investigation.

“Corporate greed motivated this pervasive misconduct. Glencore engaged in these crimes to make hundreds of millions of dollars,” Kenneth Polite,

head of the Justice Department’s Criminal Division, said in announcing the settlement. “It bribed foreign officials for business advantages across our globe, and its traders here in the United States manipulated oil benchmarks to make the company’s contracts more profitable.”

In an email to staff, Glencore Chief Executive Officer Gary Nagle said the investigations identified serious cases of past misconduct in parts of the company.

“The consequences of such conduct are damaging and costly, not only financially, but also for our reputation,” he wrote, according to a copy of the email viewed by The Wall Street Journal.

The Anglo-Swiss company has disclosed that it has set aside $1.5 billion to cover the costs of settlements in the U.S., U.K. and Brazil.

Glencore has told shareholders that it faced criminal and civil investigations from the Justice Department, Commodity Futures Trading Commission, U.K. Serious Fraud Office and the Brazilian Federal Prosecutor’s Office.

Glencore said Tuesday that it still expects to pay no more than $1.5 billion, including any additional penalties tied to the resolution of its U.K. case.

The settlement of the investigations removes a distraction for Glencore as it seeks to portray itself as the best positioned among large mining companies to capitalize on a global push to decarbonize transportation and energy. Though still a significant competitor in coal, the company has a large business in such metals as cobalt, copper and nickel, which are seen as vital to electric-vehicle batteries and the transmission of electricity.

Under the agreements announced Tuesday, the business units that pleaded guilty to U.S. criminal charges will have to hire independent compliance monitors for three years. Monitors peer into a company’s governance and compliance systems, pointing out any weaknesses and recommending ways to improve them.

The Serious Fraud Office said it had exposed bribery and corruption across Glencore’s oil operations in Cameroon, Equatorial Guinea, Ivory Coast, Nigeria and South Sudan. There, Glencore’s agents and employees paid bribes for preferential access to crude with the approval of the company, the Serious Fraud Office said in a statement.

The London court is set to sentence Glencore on June 21, the Serious Fraud Office said.

In addition to the allegations of bribery, Glencore faced the U.S. market-manipulation probe. A former Glencore oil trader pleaded guilty last year to conspiring to manipulate a benchmark tied to fuel oil used by ships.

The Justice Department and the Commodity Futures Trading Commission investigated the manipulation claims and found misconduct that spanned from 2007 to 2018. Traders tried to rig four U.S.-based physical oil benchmarks that could influence profits on futures and swaps trades linked to those reference prices, according to the CFTC.

Another former Glencore trader pleaded guilty last July to conspiring to launder money and pay millions of dollars in bribes to officials in Nigeria and elsewhere in exchange for favorable contracts with a state-owned oil company, in violation of the U.S. Foreign Corrupt Practices Act.

Anthony Stimler, a U.K. citizen, was involved from 2013 to 2015 in funneling hundreds of thousands of dollars to intermediaries to smooth Glencore’s access to Nigerian oil, according to court records. Authorities alleged that Mr. Stimler worked with co-conspirators including other former Glencore traders.

Several executives who were in their roles during the period scrutinized by authorities, including Glencore’s former CEO Ivan Glasenberg, have left the company. Mr. Glasenberg, who led the company for 19 years, declined to comment.

The investigations weighed down Glencore’s share price for several years and racked up legal costs for the company. For instance, legal costs for the first half of 2020 hit $56 million.

Glencore is still subject to investigations from Swiss and Dutch authorities.

Glencore’s share price rose 1.3% in London on Tuesday.

In the past year, the company’s share price has climbed 70% in the midst of a sizable rally in the price of the commodities it digs up, such as coal, cobalt and nickel, and as market volatility reaps profits for its large trading division.

Mr. Nagle, who succeeded Mr. Glasenberg last year, has sought to simplify the sprawling company, selling off smaller assets.

The settlements are “good news for Glencore, but there are still overhangs on the stock,” said Ben Davis, an analyst at Liberum. Those include the company’s gradual move to wind down its coal division, which is extremely profitable, Mr. Davis said.

—Sadie Gurman and Ben Foldy contributed to this article.

Write to Dave Michaels at dave.michaels@wsj.com and Alistair MacDonald at alistair.macdonald@wsj.com