The former Commons leader – who received just 11 votes last week – followed Matt Hancock in throwing her weight behind the clear favourite.
Explaining her decision, Ms Leadsom said: “The key is to keep Corbyn out. Boris Johnson will be able to do that, he will be able to unite the country.”
And she added: “He shared some of his ideas. There is no doubt he’s committed to getting us out of the EU at the end of October”
“We had a very good, detailed conversation about a managed exit. I put forward my proposals. Boris Johnson is planning carefully for how he would manage this.”
Mr Johnson’s success in wooing both Brexiteer and moderate wings of the Tory party – Mr Hancock opposes a no-deal Brexit – underlines the big lead he has on all his rivals.
He takes the support of 114 Conservative MPs into the second round of the contest today, all-but certain to be among the final two candidates to go before the Tory party membership.
However, he has been accused by Rory Stewart of telling different sections of the party what it wants to hear with contradictory versions of his Brexit plan.
In her campaign, Ms Leadsom argued there was no point in trying to renegotiate a better deal with the EU and that the UK should prepare for a crash-out Brexit on 31 October.
Describing Mr Johnson’s tactics as “alarming” Mr Stewart said: “The only way we are going to have stability in our government, or our party, or our country, is if people trust us.”
Mr Johnson also enjoys the support of self-proclaimed Brexit hardman Steve Baker, who is arguing far more than the Irish backstop needs to be stripped out of the withdrawal agreement, to make it acceptable.
He is said to have told Eurosceptics that Theresa May’s deal is “dead” – but also reassured moderate Tories there is only a very small chance of a no-deal Brexit under his premiership.
In the second round of voting, candidates need to gain at least 33 votes from MPs to remain in the race and avoid finishing in last place.
The final two will reach a run-off among the 160,000 grassroots Tory members, who will select the next prime minister.
Speaking to Talk Radio, Ms Leadsom added: “I have been to speak to each of the candidates. I have a passion for support for new families which Boris Johnson shares”
And she said: “I want to see a very diverse cabinet going forward, I want to see more women in Cabinet. Boris Johnson has supported that – I am giving him my wholehearted support.”