The Tanzanian only signed for Villa in January, with Dean Smith bringing in the striker following Wesley's season-ending knee injury.
He netted just twice in 16 appearances in claret and blue, and following the club-record signing of Ollie Watkins this summer, was likely to see first-team opportunities limited.
The deal will see Samatta head to Turkey initially on-loan, with an obligation for Fenerbahce to sign the 27-year-old permanently next summer for a fee of approximately £5.5m, potentially rising with add-ons.
"I know how big a club Fenerbahce is. Not only in Turkey, a club known and weight in the world." Samatta said.
"I am happy to be here in such a family because it will be a new and big challenge for me.
"Fenerbahce has a lot of supporters and they always want to win. I also want to win. I came with this request, I am very happy and I hope we will win many trophies."
Samatta is the second senior striker to depart B6 this summer, following Scott Hogan's move to Birmingham City. Youngster Indiana Vassilev also left the club on-loan, joining Burton Albion until the end of this season.
It leaves Watkins and Keinan Davis as the only fit senior strikers in the squad, with Wesley not expected to feature for the rest of the calendar year as he continues his recovery from injury.
Bertrand Traore is also capable of playing as an out and out striker, but is preferred in a wide role.
Dean Smith is believed to keen on adding another striker to his side before the transfer window closes next month.