The 26-year-old signed a four-year contract to return to his home city of Porto Alegre.
Anderson began his career at Internacional's city rivals Gremio in 2004 and moved to Porto when he was just 18.
He joined United from Porto in 2007 in a deal reportedly worth 27 million pounds ($40.8 million) and came on as a substitute in the 2008 Champions League final to help his team beat Chelsea on penalties.
Although he also won Premier League winner's medals, his Old Trafford career stalled as he suffered a succession of injuries and he made only 105 league appearances in nearly eight years at the club.
The Brazilian, who has played eight times for his country, was loaned to Italian club Fiorentina last year and played only two first-team games under manager Louis van Gaal this season.
(Reporting by Ed Osmond and Andrew Downie,; editing by Martyn Herman)
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