Andrea Leadsom, former leader of the House of Commons, Mark Harper and Esther McVey failed to meet the threshold of 17 votes needed to stay in the race.
Tweeting after his win, Boris said: "Thank you to my friends and colleagues in the Conservative & Unionist Party for your support".
The former foreign secretary was the clear favourite among the party's 313 MPs, storming ahead with 114 votes, 71 ahead of his nearest rival, Jeremy Hunt.
If there were only three candidates left by next Tuesday's vote, one would be eliminated and the contest could proceed to the next stage of voting by the party membership the same day, instead of next Thursday as now scheduled.
The former London mayor broke his silence to launch his campaign on Wednesday, saying he would only take Britain out of the European Union without a deal as a "last resort" as he promised to unify a country deeply divided over Brexit.
Johnson kicked off his official campaign on Wednesday with a pledge to lead Britain out of the European Union on October 31 and a warning to his divided Conservative Party that "delay means defeat".
Johnson, a former foreign secretary and leading Brexit campaigner, got 114 votes in the secret ballot among more than 300 Conservative lawmakers.
McVey is pursuing a no-deal Brexit, arguing that the agreement struck by May keeps Britain too closely tied to the European Union, while Hancock is against no-deal.
They have another round of hustings before Conservative MPs on Monday before Tuesday's second ballot, when the bar rises from 16 backers to 32, again with the contender with the fewest votes dropping out.
But Thursday's voting will reveal each candidate's current level of support.
Boris Johnson has positioned himself as the only politician certain to pass Brexit by the October 31 deadline.
"We face a crucial choice: who can negotiate some better choices than the bad ones we face", he said.
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. "That is why we are committed to taking part in the Channel 4 televised debates this Sunday and the BBC programme next Tuesday".
The Times reported the health secretary met Javid, the home secretary, but the meeting appears not to have resulted in any agreement and Hancock is now thought to be more likely to back Gove or Hunt.
After weeks of hustings around the country, the 160,000 grass-roots Conservative party members pick the victor, with the result announced in the week beginning July 22.
UK Prime Minister Theresa May resigns as leader of the Conservative Party on June 7th.
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