Lord Coe, chairman of the London Olympic and Paralympic Games, will succeed Lord Moynihan at the helm of the BOA. His position will be confirmed when the 43-member National Olympic Committee meets on November 7.
Leman, GB Hockey President, will continue to serve on the BOA board.
"Recognising the unique circumstance in which we find ourselves in having the person who led the organisation and delivery of what is widely regarded as the most successful Olympic and Paralympic Games in history standing for election as our next chair, I have decided to put my full support behind Seb Coe and his candidacy," Leman said in a statement.
'It is understood that Leman, himself an Olympic gold medallist as a member of the GB hockey team at the 1988 Seoul Games, had canvassed opinion among senior BOA figures and was advised to withdraw gracefully to avoid inevitable defeat' Daily Telegraph reported.
