Pereira has signed a four-year contract, with the option of a further year, for an undisclosed fee.
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Pereira, 26, said: "I'm very happy to be here and I can't wait to start the season with Fulham.
"I want to help Fulham as much as I can be to where they belong. Marco Silva was very important for this. I spoke a lot with him, and he was a key factor in me being here."
Pereira spent last season back in his home country of Brazil on loan at Rio de Janeiro giants Flamengo, but the teams failed to agree a permanent deal.
After joining from PSV Eindhoven in 2012, Pereira came through the youth ranks at Old Trafford before making his first-team debut in 2014. However, he was unable to hold down a regular first-team place and also spent time on loan at Granada, Valencia and Lazio.
Pereira made only 45 appearances in the Premier League, just 24 of them starts, scoring two goals. He had a year remaining on his Man United contract.
Pereira's departure comes with United set to sign Christian Eriksen on a free transfer. Sources have told ESPN that the Denmark international will sign a three-year deal upon the completion of a medical following the end of his short spell with Brentford last season.
United are also pursuing Barcelona midfielder Frenkie de Jong, with sources telling ESPN last week that the clubs had agreed an initial €65 million fee. But Barcelona president Joan Laporta has insisted that he will do everything to get De Jong to stay at the Camp Nou, despite the club's financial difficulties.
Pereira will add further Premier League experience to a Fulham side that gained promotion from the Championship last season. They have already signed midfielder Joao Palhinha from Sporting Lisbon for a reported £20m fee.