The former business secretary, 53, said Brexit gave Britain the freedom to show “global leadership” over Ukraine, making it “impossible for Putin to succeed”.
Mr Rees-Mogg told Sky News’ Sophy Ridge on Sunday: “Putin would probably have invaded Ukraine successfully if the UK had been bound in by the requirement of sincere co-operation and had had to follow a Franco-German line in dealing with Russia, which is what we did in 2014.
“I think the leadership shown by (former prime minister) Boris Johnson, which he could only do because he was not bound by sincere co-operation, ensured that a coalition was set up that made it impossible for Putin to succeed.”
He also said it was a mistake to get rid of Mr Johnson, but deposing Rishi Sunak would be an “even bigger” one.
“The Tory party would be toast if we change leader again… but that doesn’t mean we agree with him on every policy,” Mr Rees-Mogg said.
Mr Johnson had also said that leaving the EU allowed Britain to “do things differently” in providing weapons to Ukraine.
Speaking at an event in Washington DC in February, he said: “I seriously think that it was in part because of Brexit that we were able to take a decision and to have an approach that was very distinct from the old EU approach, which was, by the way, all governed by the fabled Normandy Format, which was agreed in Normandy in 2014.
“For reasons that are now obscure to me, the British government decided they did not want to be involved in this. France and Germany led it, that was the EU framework.
“If we’d stuck with that, I don’t believe we would have delivered the NLAWs [anti-tank weapons] and I think we would have taken a very different approach, to be perfectly frank.
“I think because of Brexit we’ve been able to do things differently and I hope in a way that has been useful to Ukraine,” Mr Johnson added.
The UK has commited £4.6billion in military aid to Ukraine so far.
The UK is also providing long-distance precision strike missiles, tanks and aims to train 30,000 new and existing Ukrainian personnel by 2023.