Fallon attacked Gani during the London Mayoral campaign, echoing a claim made by David Cameron in parliament that the imam backed the extremists.
The false claims of Gani's links with Islamic State were repeated during campaigning as then-Tooting MP Sadiq Khan faced off against Zac Goldsmith.
Although Cameron's comments were in the House of Commons, and therefore protected by parliamentary privilege, the Prime Minister later issued a formal apology, while Gani launched legal action against Fallon, whose comments were made on BBC Radio 4's Today programme.
Fallon had previously apologised to Gani, saying he was repeating a claim made on the BBC, but was unaware the broadcaster had issued a correction and also apologised.
And in a statement, the defence secretary has revealed he will also pay the imam's legal costs and pay compensation.
“I accept that you are entirely opposed to Daesh/Islamic State, that you regard it as incompatible with your religious and moral beliefs, and that you have spoken out publicly against it,” Fallon said.
“I repeat my apology for the error that I made and for the distress that it caused to you and your family.”