Johnson has promised to leave the European Union with or without a deal on the October 31 deadline.
Like Johnson, Raab and Javid have said they would not rule out a "no-deal" Brexit.
Bookmakers Ladbrokes have slashed their odds of Boris Johnson replacing Theresa May as Prime Minister to 1/5, while Betfair is now offering odds-on at 2/7 for him to win. A total of 313 lawmakers voted.
"Thank you to my friends and colleagues in the Conservative & Unionist Party for your support".
In a joint statement, Jeremy Hunt, Michael Gove, Dominic Raab, Sajid Javid, Matt Hancock and Rory Stewart said the leadership contest was "a critical moment" for both the United Kingdom and the Conservative party.
Sajid Javid, interior minister, came fifth with 23 votes.
International Development Secretary Rory Stewart snuck through in seventh place with 19 votes after running an original social media campaign that endeared him to more liberal party members - and the British public at large.
Andrea Leadsom, Esther McVey and Mark Harper didn't receive enough votes to progress and were eliminated from the contest.
Betting markets give Johnson, who has a long record of scandals and gaffes, a 70% probability of winning the top job.
The BBC's political editor Laura Kuenssberg said there was plenty of time for the maths in the contest to change fundamentally but the first round of voting should provide a better idea of how the numbers are shaping up.
Conservative legislators will hold further elimination rounds of votes next week until two contenders remain. But she will stay on as a lame duck Prime Minister until her successor is chosen. There had been speculation that the contest could be accelerated due to Johnson's strong lead but there was no immediate sign of rivals bowing out of the race. "This serious moment calls for a serious leader", he tweeted.
"This campaign is just getting started, and we've got a good base to build on", he said. It's increasingly clear it's me against Boris.
At the next round of voting on June 18, candidates will need 33 votes to remain in the contest.
She stepped down as the centre-right party's leader on Friday, having failed to deliver her plan for taking Britain out of the European Union after almost three years in the post.
Speaking at his leadership launch event on Wednesday, Mr Johnson said: "I am not aiming for a no-deal outcome".
The two candidates most keen on taking Britain out of the European Union without a deal were eliminated.
PM hopeful Michael Gove runs close to his home in London, Britain, June 13, 2019.
But the European Union has refused to renegotiate the Withdrawal Agreement reached with May last November and Ireland has said it is not willing to change the backstop.
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