He said “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.
“But I must tell you, my friends … that having consulted colleagues and in view of the circumstances in parliament, I have concluded that person cannot be me.”
He was seen by many as the favourite to succeed the Prime Minister.
Earlier, justice secretary Michael Gove announced he would be standing as he felt Mr Johnson isn’t up to the job.