Mr. Browne, who had already moved up his departure by more than a year after a deadly refinery blast in Texas and a giant oil spill in Alaska, denied any improper conduct relating to BP, but he acknowledged that he had lied to a judge about how he met his former partner, with whom he had a four-year relationship.
The Mail on Sunday, the newspaper that sought to publish the claims, immediately called for Mr. Browne to be prosecuted for perjury and said it would provide evidence of his deception to the attorney general's office.
Mr. Browne said he regretted the lie, saying he was in shock at his private life being exposed and that he was stepping down voluntarily "to avoid unnecessary embarrassment and distraction to the company."
"For the past 41 years of my career at BP I have kept my private life separate from my business life," he said.
Mr. Browne's designated successor, exploration and production head Tony Hayward, will take over as CEO immediately, the company said. He will have to repair BP's tarnished reputation after the series of high-profile operational and regulatory mishaps.
BP said Mr. Browne's decision meant he would lose a bonus of as much as 1.3 times his annual salary, worth more than $6.9 million. He would also forgo inclusion in a share plan with a potential value of $23.9 million.
Mr. Browne, 59, had been fighting since January to keep the Mail on Sunday from publishing details from the interview with Jeff Chevalier.
Mr. Browne was accused of using BP computers and staff to help Mr. Chevalier, of using support staff to set up and then wind down a company Mr. Browne created for him to run, and sending a senior BP employee on a personal errand to deliver cash to him.
Mr. Browne rejected the allegations, calling them "full of misleading and erroneous claims. I deny categorically any allegations of improper conduct relating to BP."
BP said an internal investigation determined those allegations were unfounded.