Tony Hayward, the embattled chief executive of BP, has agreed to step down and be replaced by Robert Dudley, the company's most senior American executive who is now in charge of BP's operations in the Gulf of Mexico, according to a person close to the company's board.

The change in leadership will be discussed by the board of directors on Monday and may be announced Tuesday if the board ratifies the decision. Mr. Hayward would probably be replaced in the fall, the person said, but a decision has already been made by mutual agreement between Mr. Hayward and senior BP management.