Three contenders – Mark Harper, Andrea Leadsom and Esther McVey – were knocked out in the secret ballot of Tory MPs.
Mr Johnson received 114 votes, significantly more than his nearest rival Jeremy Hunt, who came second with 43. Michael Gove was third with 37.
Seven candidates progress to the next round of voting next week.
The two who prove most popular after the last MPs’ ballot will go to Conservative Party members in a final vote later this month.
The winner of the contest to succeed Theresa May is expected to be announced in the week of 22 July.
Sources close to Health Secretary Matt Hancock told the BBC’s Laura Kuenssberg he was “mulling over” whether to withdraw from the contest after coming sixth with 20 votes.
Home Secretary Sajid Javid, who came fifth with 23 votes, is understood to be staying in the race for now. Some have suggested his candidacy – with support from Mr Hancock – could take on Mr Hunt to become second in the ballot.