Jes Staley stepped down as chief executive of Barclays PLC under pressure from regulators about how he characterized his relationship with the convicted sex offender and financier Jeffrey Epstein.

Barclays said Mr. Staley stepped down “in view of the conclusions” made by U.K. regulators in its long-running investigation into what Mr. Staley told the bank about his association with Epstein and what it told regulators about the relationship. Barclays shares fell 0.7% Monday.

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Jes Staley stepped down as chief executive of Barclays PLC under pressure from regulators about how he characterized his relationship with the convicted sex offender and financier Jeffrey Epstein.

Barclays said Mr. Staley stepped down “in view of the conclusions” made by U.K. regulators in its long-running investigation into what Mr. Staley told the bank about his association with Epstein and what it told regulators about the relationship. Barclays shares fell 0.7% Monday.

The probe concluded that Mr. Staley provided an incomplete picture of his relationship with Epstein, which the board passed on to the regulator, according to people familiar with the investigation.

The bank said the investigation didn’t find evidence that “Mr. Staley saw, or was aware of, any of Mr. Epstein’s alleged crimes” and said Mr. Staley was planning to contest the conclusions made by regulators.

“I do not want my personal response to those matters to be a distraction from the fantastic work you do every day to support our customers and clients,” Mr. Staley wrote to staff in an internal memo.

C.S. Venkatakrishnan, head of global markets, will take over as chief executive immediately, the bank said.

Spokespeople for the U.K.’s Financial Conduct Authority and Prudential Regulation Authority confirmed the Barclays statement but declined to provide further details about the investigation.

“It appears regulators believe there was a distinct lack of transparency over this relationship,” said Susannah Streeter, an analyst at U.K. asset manager and stockbroker Hargreaves Lansdown.

Mr. Staley has said his relationship with Epstein was professional and began in 2000 when he was head of the private bank at JPMorgan Chase & Co. and the financier was a client. He told journalists in February 2020 that his interactions with Epstein began to “taper off” after he left JPMorgan in 2013 and that the last time he had contact with him was in the “middle to fall” of 2015. He became Barclays CEO in December 2015.

Jeffrey Epstein was found dead in 2019 at a New York detention center where he was awaiting trial on federal sex-trafficking charges.

Photo: /Associated Press

The Wall Street Journal reported in March 2020 that Mr. Staley, who had a large custom-designed sailboat, visited Epstein’s private Caribbean island twice with his wife.

The bank disclosed the existence of the FCA investigation in February 2020. At the time, Mr. Staley said of Epstein: “I thought I knew him well and I didn’t…For sure, with hindsight, with what we all know now, I deeply regret having had any relationship with Jeffrey Epstein.”

Barclays said board members were disappointed that Mr. Staley was stepping down. Mr. Staley, 64, said a year ago that he intended to stay at the bank for a couple more years.

Mr. Staley had a bumpy tenure as CEO. He joined the bank in 2015 and struggled to convince investors about the bank’s business model. He saw Barclays as a mini-version of JPMorgan, with a retail bank—one of the U.K.’s largest—combined with a sizable trans-Atlantic investment bank.

The bank’s share price has fallen about 10% since Mr. Staley took charge.

Barclays is the U.K.’s last remaining investment bank that competes on Wall Street with the likes of Goldman Sachs Group Inc. and JPMorgan. It acquired parts of Lehman Brothers during the financial crisis and has a large U.S. credit-card business.

During his tenure, Mr. Staley streamlined operations and cut thousands of jobs. He appointed fellow former JPMorgan bankers to senior positions, including Mr. Venkatakrishnan.

He also saw the bank through Brexit and the Covid-19 pandemic.

The Epstein probe was the second brush with U.K. authorities for Mr. Staley, an American. In 2018, he was hit with penalties equal to about a quarter of his 2016 pay over his efforts to unmask a whistleblower, which U.K. regulators called a “serious error of judgment.” U.S. authorities also fined him over the episode.

He then faced a campaign from activist investor Edward Bramson, who pushed Barclays to slash its investment banking business and criticized Mr. Staley for his relationship with Epstein. Mr. Bramson’s Sherborne Investors sold its 6% stake in Barclays earlier this year. Investment banking profits boomed during the coronavirus pandemic, appearing to vindicate Mr. Staley’s strategy.

At issue with Mr. Staley was the version of interactions with Epstein that he presented to Barclays and the version the bank gave to regulators.

Jeffery Epstein's estate on Little St. James island.

Photo: Gianfranco Gaglione/Associated Press

Barclays said last year that Epstein’s death in 2019 had renewed interest in Mr. Staley’s dealings with him and that the CEO gave an explanation to executives, including Chairman Nigel Higgins. Mr. Staley confirmed he had no contact with Epstein after becoming Barclays’s CEO, the bank said.

U.K. regulators also asked the bank about the relationship, Barclays said in February 2020. The FCA and the PRA began an investigation into Mr. Staley’s description to Barclays of his relationship with Epstein and the subsequent description of that relationship to the FCA.

They relied on a trove of emails and other documents handed over by Mr. Staley’s former employer, JPMorgan, people familiar with the investigation said, the Journal reported in March 2020.

The Journal also reported at the time that Barclays employees had expressed concerns to the regulators about the truthfulness of disclosures made by Mr. Staley and the bank, according to people familiar with the FCA probe.

Mr. Staley is one of a string of high-profile executives to face scrutiny over ties to Epstein. Earlier this year, Leon Black stepped down as chief executive of Apollo Global Management Inc. after a review revealed larger-than-expected payments to Epstein in exchange for trust-and-estate-tax advice.

The review found no evidence that Mr. Black was involved in the criminal activities of the late Epstein.

Bill Gates’s relationship with Epstein was a source of concern for Melinda French Gates in the run-up to announcing the couple’s divorce, the Journal reported. Mr. Gates said he met multiple times with Epstein to discuss philanthropy and regretted ever meeting him.

The coming trial of British socialite Ghislaine Maxwell on counts related to her alleged role in Mr. Epstein’s sex-trafficking network, could reveal new information about Mr. Epstein’s relationships across Wall Street and beyond, people familiar with the case said. The trial is slated to start in the coming weeks. Ms. Maxwell has pleaded not guilty. Her lawyers have said in court papers that much of the alleged conduct is decades old and have called witnesses’ memories unreliable.

Epstein pleaded guilty in Florida state court to soliciting prostitution from an underage girl in 2008. He was found dead in August 2019 at a New York detention center where he was awaiting trial on federal sex-trafficking charges, in what the New York medical examiner ruled a suicide.

In 2020, prosecutors in the U.S. Virgin Islands alleged Epstein abused hundreds of young women and girls until 2018. The prosecutors said that for nearly two decades, Epstein brought girls as young as 11 to his secluded property on Little St. James island.

JES STALEY AND JEFFREY EPSTEIN: A TIMELINE

2000: Mr. Staley, then head of JPMorgan’s private bank, meets Epstein, a client of the bank, Mr. Staley says. A person close to their association says Epstein subsequently introduces Mr. Staley to wealthy people and recommends JPMorgan to them, including Glenn Dubin, co-founder of hedge fund Highbridge Capital Management.

2004: JPMorgan buys control of Highbridge for more than $1 billion. Epstein earns a fee of around $15 million from Highbridge, according to people familiar with the payment.

2008: Epstein pleads guilty to two prostitution offenses in Florida state court.

2013: Mr. Staley leaves JPMorgan. He remains in contact with Epstein.

2015: Mr. Staley is in contact with Epstein until mid-to-late fall, Mr. Staley says. Mr. Staley becomes Barclays CEO in December.

2019: Epstein dies in jail in New York. Mr. Staley gives Barclays executives, including Chairman Nigel Higgins, an explanation of his relationship with Epstein. Barclays responds to a U.K. regulator’s inquiry about the relationship.

2020: Barclays discloses a formal U.K. regulatory investigation into Mr. Staley’s relationship with Epstein. The investigation is ongoing.

2021: Mr. Staley resigns as CEO.

—Margot Patrick contributed to this article.

Write to Simon Clark at simon.clark@wsj.com and Emily Glazer at emily.glazer@wsj.com