Lord Browne tendered his resignation after the lifting by the UK courts of a legal injunction preventing a newspaper group from publishing details of his private life.
Lord Browne said: "In my 41 years with BP I have kept my private life separate from my business life. I have always regarded my sexuality as a personal matter, to be kept private. It is a matter of deep disappointment that a newspaper group has now decided that allegations about my personal life should be made public.
"Concerning the court documents disclosed today, I wish to acknowledge that I did have a four-year relationship with Jeff Chevalier who has now chosen to tell his story to Associated Newspapers, publishers of The Daily Mail, Mail on Sunday and Evening Standard.
"These allegations are full of misleading and erroneous claims. In particular, I deny categorically any allegations of improper conduct relating to BP."
BP chairman Peter Sutherland said that Lord Browne had informed the company of allegations relating to the limited use by Jeff Chevalier of BP computer and staff resources.
Mr. Sutherland said: "At John's explicit request, the board instigated a review of the evidence. That review concluded that the allegations of misuse of company assets and resources were unfounded or insubstantive.
"John has made it clear to the BP Board that he has decided to step down with immediate effect because he does not want this public focus on his private life to detract from the paramount task of running the BP group.
"The Board of BP has accepted John's resignation with the deepest regret. For a chief executive who has made such an enormous contribution to this great company, it is a tragedy that he should be compelled by his sense of honor to resign in these painful circumstances."
The company said that as a result of Lord Browne's decision to resign he would lose his agreed entitlement to a year's notice including a bonus of up to 1.3 times his annual salary, worth in total over £3.5 million. He would also forego inclusion in the long-term performance share plan for 2007-2009 with a maximum potential value of some £12 million.
Personal statement by Lord Browne of Madingley
"For the past 41 years of my career at BP I have kept my private life separate from my business life. I have always regarded my sexuality as a personal matter, to be kept private.
"It is a matter of personal disappointment that a newspaper group has now decided that allegations about my personal life should be made public.
"Legal documents have been disclosed today containing allegations about me and my personal life. I wish to acknowledge that I did formerly have a four-year relationship with Jeff Chevalier. He has made these allegations about me and our relationship to Associated Newspapers, publishers of The Daily Mail, Mail on Sunday and Evening Standard.
"The allegations are full of misleading and erroneous claims. I deny categorically any allegations of improper conduct relating to BP. The company has confirmed today that it has found no such wrongdoing.
"My initial witness statements, however, contained an untruthful account about how I first met Jeff. This account, prompted by my embarrassment and shock at the revelations, is a matter of deep regret. It was retracted and corrected. I have apologized unreservedly, and do so again today.
"These allegations will result inevitably in considerable media attention for both myself and BP. What matters to me is BP, what we have achieved during my tenure and the bright future ahead.
"I have therefore informed the Board of BP that I intend to stand down as group chief executive with immediate effect, rather than retiring at the end of July. This is a voluntary step which I am making to avoid unnecessary embarrassment and distraction to the company at this important time.
"I have spent my entire working life with BP, and want to thank everyone for their dedication, loyalty, support and hard work in creating one of the world's finest companies.
"I shall not be commenting on my personal issues further. I wish to pursue my personal life in private."
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