The two most popular MPs will be put to party members in a final vote later this month.
His next closest rival Jeremy Hunt was nearly seventy votes behind him, closely followed by Michael Gove. Others remaining in the race are Dominic Raab (27 votes), Sajid Javid (23), Matt Hancock (20), and Rory Stewart (19).
Mark Harper, the former immigration minister who resigned after finding out his cleaner was not legally allowed to work in the United Kingdom, followed McVey out of the race, garnering just 10 votes.
Sir John Major has been scathing of suggestions the incoming Prime Minister could suspend Parliament to prevent it blocking a no-deal Brexit.
He said: "Thank you to my friends and colleagues in the Conservative & Unionist Party for your support".
Johnson got 114 votes.
A third ballot will take place on June 19, with provision for a fourth and fifth ballot on June 20 if necessary.More news: Eden Hazard Joins Real Madrid on a Five-Year Contract
More news: UK Approves US Request For Julian Assange's Extradition
More news: Binnington's legendary performance secures Blues' first-ever Stanley Cup
After weeks of hustings around the country, the 160,000 Conservative party members then choose their favourite, with the result announced in the week beginning July 22.
The victor will take over from Theresa May as the next British Prime Minister. 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".
Finance minister Philip Hammond, who has not publicly endorsed a candidate, wrote on Thursday to all remaining leadership contenders to urge them to stick to existing budget rules until at least the next scheduled election in 2022. It's increasingly clear it's me against Boris.
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.
PM hopeful Michael Gove runs close to his home in London, Britain, June 13, 2019.
All the Conservative contenders say if they emerge as the victor, they will renegotiate the contentious Brexit withdrawal agreement Theresa May struck with Brussels last November after two years of ill-tempered haggling. No deals have yet been done, the sources said.