Former Tory leadership candidate Mr Stewart said he has resigned from the Conservative Party and will stand down at the next general election.
The eventful first PMQs for Mr Johnson follows a humiliating defeat that forced him to hand control of the Commons to MPs opposed to no-deal Brexit.
The justice secretary is one of a number of ministers who plan to resign once Boris Johnson is named prime minister.
Mr Johnson’s seemingly inexorable journey to victory saw him win 126 votes from Tory MPs.
A second round of voting in the Tory leadership race takes place ahead of a live TV debate on BBC this evening.
Rory Stewart has gone from an outsider in the Tory leadership contest to second favourite behind Boris Johnson.
The minister for international development is one of ten candidates to be Tory leader.
The PM is under pressure to avoid another backlash like the one she received when replacing Sir Michael Fallon as Defence Secretary with Gavin Williamson.