The former foreign secretary is now supported by nearly a third of party members, according to a monthly poll of 1,000 Tories by the website ConservativeHome.
Just a month ago, before his July 9 resignation over the Chequers Brexit proposals, Mr Johnson was backed by only 8 per cent of members.
He is nearly ten points ahead of his nearest rival, Home Secretary Sajid Javid.
Environment Secretary Michael Gove’s support slumped to 7 per cent following his failure to quit in the aftermath of the Chequers deal.
Under Tory leadership rules, MPs get to choose the final two candidates whose names will go into a head-to-head contest, with votes cast by grassroots Tory members.
When the Uxbridge MP resigned, he wrote that Mrs May’s blueprint would leave the UK in ‘vassalage, satrapy, colony status’ to the EU.
‘It can’t and won’t work. Chuck Chequers,’ he added.
In his resignation speech in the Commons, the former foreign secretary said the Prime Minister had ‘dithered’ over Brexit and there had been ’18 months of stealthy retreat’.
He said her Chequers plan would lead to ‘Brexit in name only’ and leave Britain in a ‘miserable, permanent limbo’.
Although Mr Johnson stopped short of making a direct challenge to Mrs May in his 12-minute personal statement, he did warn her to change direction.
He declared it was ‘not too late to save Brexit’ – and made it clear he stood ready to lead the charge to ensure a clean break with the EU this autumn.
Mr Johnson flouted ‘revolving door’ rules that ban ex-Cabinet ministers from taking up new appointments in the three months after leaving office.
Under the ministerial code, former ministers must apply to the Advisory Committee on Business Appointments (Acoba) before accepting a new role.
The rules also stop ministers who have been members of the Cabinet from starting new appointments in the first three months after stepping down.
Mr Johnson, who gave up his £275,000-a-year newspaper column when he was appointed foreign secretary in July 2016, made his comeback last month with an article arguing that Britain must believe in itself after Brexit.