The 25-year-old has been in talks with West Londoners over the last 24 hours, with a £12m fee believed to have been agreed between the two clubs.
It had been claimed that West Ham United were keen to hijack the deal, but Fulham have now confirmed that they have won the race for the 28-time Greece international's signature.
"I'm very happy that I'm here in the Premier League, and especially with Fulham which is a major club in the league," Mitroglou told the club's official website. "I'm here because I want to fulfil the club's targets and I want to help the club achieve their goals. I was really flattered that they wanted me so badly and I'm really happy to be here.
"I'm really happy that I will work with Rene Meulensteen. I know that he has a lot of experience in football. He explained to me how he works and I am really looking forward to working with him."
Should the rumoured fee be correct, Mitroglou has become Fulham's record signing.