Fred spent five years at Old Trafford after joining from Shakhtar Donetsk in 2018 but was informed his playing time under Erik Ten Hag will be reduced this season.
The 30-year-old costs Fenerbahce £13m.
Fred made 213 appearances for Manchester United during his time at the club and scored 14 goals.
"Today ends one of the most beautiful stages of my career," Fred said on social media.
"I lived the dream of wearing the shirt of one of the biggest clubs in the world."
"Going through ups and downs, I leave with the conviction that I always gave my best during all training sessions and games.
"It was five years of a true dream for me and my family. I will be forever grateful for the opportunity. Forever a Red!"
"I am very happy to come to Turkey's biggest club with such a great history. I want to be a part of this history too," Fred told Fenerbahce's website.
"My first impressions are very good and positive. Everyone at the club made me feel very welcome. I was extra happy for that too.
"I also want to play big by doing my best, win all the trophies and contribute to all successes. Of course, I want to make the fans happy.
"Now I will play for Fenerbahce fans on this field here. I cannot wait for this. Fenerbahce fans started to support me even before I came here. I will do my best. Let no one doubt that.
Fred's only trophy with Manchester United was last season's Carabao Cup triumph over Newcastle United.
