Johnson is favored to defeat British Foreign Secretary Jeremy Hunt in the voting that ended Monday night.
The new prime minister will officially replace Theresa May on Wednesday as she steps down following repeated failures to deliver Britain’s exit from the European Union.
The Brexit process was meant to be concluded in late March, but while EU officials have indicated no interest in renegotiating the divorce terms that Britain’s parliament has rejected three times so far, they did agree to push the deadline to October 31.
Johnson, a populist former foreign secretary under May and mayor of London, has expressed a willingness to withdraw Britain from the EU at that time with or without an agreement in place. Many members of parliament oppose a no-deal Brexit, saying such a move would be economically chaotic.