Lord Browne, chief executive officer at oil giant BP, has tendered his resignation with immediate effect after failing to prevent details over his private life entering the public domain.
A legal injunction stopping a newspaper group from publishing a story about the 59-year-old's personal life was recently lifted by UK courts.
Lord Browne, who had already announced he would leave BP in July, stands to lose a retirement package worth at least £3.5 million, although it could have risen to £12 million.
"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," the BP chief said in a statement released through the oil group.
"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," the statement continued.
"These allegations are full of misleading and erroneous claims. In particular, I deny categorically any allegations of improper conduct relating to BP."
A BP review conducted in response to Mr Chevalier's media claims found the allegations of company misuse were "unfounded or insubstantive".
BP chairman Peter Sutherland said: "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 honour to resign in these painful circumstances."
Dr Tony Hayward has been appointed as Lord Browne's successor.