Former London Mayor Boris Johnson, who had been considered one of the favourites to replace David Cameron as British Prime Minister, says he won't be standing.
In his speech, Mr Johnson said the Brexit decision was the nation's chance to "think globally again".
"To lift our eyes to the horizon, to bring our unique British voice and values - powerful, humane, aggressive - to the great global forums without being elbowed by a supranational body."
He said while that was the agenda for the next Prime Minister, it wouldn't be him.
"Having consulted colleagues, and in view of the circumstances of parliament, I have concluded [the Prime Minister] cannot be me."
Mr Johnson pledged support for the next leader of the Conservative Party.
The shock announcement came after fellow Leave campaigner Michael Gove threw his hat in the ring for the party leadership.
In a statement, Mr Gove said he had wanted to help build a team behind Mr Johnson so a politician who argued to leave the EU could lead the nation "to a better future".
"But I have come, reluctantly, to the conclusion that Boris cannot provide the leadership or build the team for the task ahead."
Late last week it was speculated justice minister Mr Gove would back Mr Johnson for the position of UK Prime Minister.
Mr Cameron announced on Friday he would step down as Prime Minister after voters chose to leave the EU in a historic referendum. He had urged voters to remain in the bloc.
Interior minister Theresa May has also entered the leadership contest, and she is likely to get support from allies of Mr Cameron.
Despite campaigning to remain in the EU, in a statement she said Britain must stick to the results of the vote.
"The country voted to leave the European Union, and it is the duty of the Government and of Parliament to make sure we do just that."
The official nominations for the Conservative party leadership are Mr Gove, Ms May, energy minister Andrea Leadsom, former defence secretary Liam Fox and work and pensions secretary Stephen Crabb.