The party wants a vote to happen tomorrow, so Mr Johnson leaves office before the Conservative Party selects a new leader.
Those hoping to be the next Tory leader have until 6 o'clock tonight to submit their applications.
Candidates need to have 20 supporters in order to continue in the race.
Deputy PM and Esher MP Dominic Raab has come out in support of Rishi Sunak, as has Fulham's Greg Hands.
Yesterday evening, Runnymede's Dr Ben Spencer declared his support for Tom Tugendhat.