In his dramatic speech, Mr Johnson said the “agenda” of David Cameron’s replacement as prime minister would be to “think globally again”.
He said: “This is our chance to think globally again to lift our eyes to the horizon to bring our unique British voice and values – powerful, humane, progressive – to the great global forums without being elbowed aside by a supranational body.
“And instead of being afflicted by inertia let us seize this chance and make this our moment to stand tall in the world, that is the agenda for the next Prime Minister of this country.”
Mr Gove will now battle for Downing Street with fellow challengers Mrs May, Mrs Leadsom, Work and Pensions Secretary Stephen Crabb and former defence secretary Liam Fox.
Both Health Sectretary Jeremy Hunt and Education Secretary Nicky Morgan today said they will not be running for the Tory leadership, with nominations closing at midday.
Mr Hunt gave his support to Mrs May while Ms Morgan will back Mr Gove.