The 25-year-old midfielder, who has the option to extend his time at Old Trafford by an additional year, joins from Shakhtar Donetsk for a reported £52m, including add-ons.
Fred follows Diego Dalot as United's second signing of the summer.
Upon his unveiling, the Brazilian said: “This is the biggest club in the world and I am delighted to be a part of this amazing team. To work with 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.
“This is a very exciting time for me with my focus now fully on the World Cup with Brazil.”
Manager Jose Mourinho added: “Fred will complement our other midfielders' qualities, which we need; his creative brain and passing vision will give us another dimension to our game.
"I am very happy he is joining our club and I believe our players know how important he can be in our team.”
Fred is currently on duty with Brazil at the World Cup in Russia but has yet to feature for Tite's side, having remained unused as a substitute in the South Americans' opening game against Switzerland.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies