"I can't envisage a circumstance where a CEO stays beyond the agreed period", he said.
Mr. Rolet had originally planned to retire at the end of next year, giving the exchange operator, one of Europe's biggest, time to find a replacement.
The board of the London Stock Exchange (LSE) has today accused activist hedge fund TCI of "damaging" the bourse's reputation, through its efforts to reinstate outgoing boss Xavier Rolet.
The company said that David Warren, its chief financial officer, would become interim chief executive after Mr Rolet's sudden exit.
TCI could pursue its desire to stage an EGM with the aim of removing Mr Brydon immediately, but this would lead to the publication on Thursday of a circular expected to contain details of previous boardroom tensions.
The LSE said it has asked TCI to withdraw its proposal for an extraordinary meeting.
Rolet's departure after 8-1/2 years in charge could trigger fresh speculation that a rival exchange such as ICE (ICE.N) could bid for the LSE, though analysts say any mega-bourse deal would face intense scrutiny by competition authorities.
On Tuesday, Bank of England governor Mark Carney said he was "mystified" by the dispute and said it was "in the interest of all parties that clarity is provided as soon as possible". I will not be returning to the office of CEO or director under any circumstances.
Chairman Donald Brydon has indicated that he will not stand for re-election at the annual general meeting in 2019, the company added.
Mr Rolet's departure comes after eight years in the top job, during which time the LSE has seen its stock market value soar from £800 million to almost £14 billion. It will also contain potentially negative details about Mr Rolet's management style that the board will use to protect itself against accusations it wrongly forced the chief executive to leave.
The fund had been urging Mr Brydon to resign on his own terms, for Mr Rolet's contract to be extended and for the group to suspend the search for his successor.