He is expected to be replaced by the American Bob Dudley, who is in charge of the cleanup operation.
Hayward has been widely criticised over his handling of the disaster following a series of gaffes.
US President Barack Obama and residents of the Gulf coast hit out at Hayward when he said in June that he “wanted his life back” and that the Gulf was “a big ocean”.
Hayward and BP could be in line for further criticism after he departs.
The terms of his contract entitle him to a £1m payout, while his pension pot is said to be worth as much as £11m.
BP is expected to report a $13bn (£8.4bn) loss when it announces second quarter results tomorrow (27 July) as the costs of cleaning up the oil spill mount.
Figures are said to include compensation and cleanup costs of up to £19bn.
BP insists that no final decision has been made over Hayward’s future. The company adds that a board meeting is being held later today and “any decisions will be announced as appropriate”.