The Brazil international's contract was due to expire next summer.
The 30 year old leaves Old Trafford having made 213 appearances for the club since joining from Shakhtar Donetsk in 2018.
"Thanks for everything, Manchester United Football Club," said Fred in a social media post.
“Today ends one of the most beautiful stages of my career. 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!”
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