The midfielder, who has signed a four-year deal, joined the Reds in 2007 from FC Porto and helped the team win the Champions League in his first season, memorably firing home a crucial penalty during the shoot-out with Chelsea in Moscow.
Despite appearing regularly during the summer tour, he has made only one Barclays Premier League appearance this term, as a substitute at Burnley in August. The 26-year-old also started the previous fixture - the Capital One Cup defeat at Milton Keynes Dons.
Formerly with Gremio, he is heading back to his home town of Porto Alegre and his farewell performance for the club came in the Under-21s' 2-1 victory over Liverpool last Monday.
Everybody at United would like to wish Anderson the best of luck for the future