The ex-PM urged his supporters to stick with the agenda he set out to deliver victory at the next general election.
The next prime minister will start assembling a top team that he will hope can return a measure of stability to the country.
The former chancellor spoke at Conservative Party headquarters. Here is a transcript of his address.
The former chancellor will become the first non-white prime minister, the first Hindu in the top job and also arguably the richest occupant of No 10.
Mr Johnson was forced late on Sunday to admit he could not unite his warring party, seemingly surrendering to Rishi Sunak.
The SNP Westminster leader’s comments come after Boris Johnson’s dramatic withdrawal from the Tory leadership contest.
Northern Ireland minister Steve Baker, an influential figure on the Tory right, is backing former chancellor Rishi Sunak.
Scottish Deputy First Minister John Swinney made the call as the deadline approaches for candidates to declare in the Tory leadership contest.
The former chancellor became the second candidate to declare their prime ministerial ambitions.
The ex-chancellor lost out to Liz Truss in the last leadership contest just six weeks ago after warning her tax plans would bring turmoil.