LONDON (Reuters) - Boris Johnson, one of the leaders of the successful "Leave" campaign in Britain's European Union membership referendum, has won the backing of a key colleague to replace David Cameron as prime minister, a newspaper reported.

Justice minister Michael Gove called Johnson by telephone on Saturday to say he would back him for the leadership of the ruling Conservative Party, the Sunday Times said.

Cameron announced on Friday that he would step down as prime minister by October after voters in the referendum took the historic decision to back the "Leave" campaign which was led by Johnson and Gove. Cameron had urged voters to stay in the bloc.

The Sunday Times said the home secretary Theresa May was expected to enter the leadership contest in the coming days and was likely to get support from allies of Cameron who see her as the best candidate to take on Johnson, a former London mayor.

May supported the "Remain" campaign but took a lower profile than Cameron and Chancellor of Exchequer George Osborne, whose hopes of becoming the party's next leader took a big blow with the outcome of the referendum.

(Writing by William Schomberg)