"This is the biggest club in the world and I am delighted to be a part of this amazing team," Fred told United's website.
"To work with (manager) Jose Mourinho, who has won so many trophies in his time as a coach, is an opportunity not to be missed.
"I cannot wait to get started and to meet my new team-mates. I would like to thank everyone at Shakhtar Donetsk for everything they have done for me over the past five years."
Fred is in the Brazil World Cup squad, but was an unused substitute for the 1-1 draw with Switzerland in their opening game.
Fred will compete for a midfield place with Paul Pogba and Nemanja Matic next season as United aim to challenge champions Manchester City for the Premier League title.
"Fred will complement our other midfielders' qualities, which we need; his creative brain and passing vision will give us another dimension to our game," Mourinho said.
Fred won three Ukrainian league titles with Shakhtar after joining from Brazil's Internacional in 2013.
United also signed Portuguese full back Diogo Dalot from Porto this month.
(Reporting by Anirban Paul in Bengaluru, editing by Ed Osmond)
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