The Porto Alegre-based club have confirmed the news on their official website, meaning the 26-year-old ends his seven-year spell at the Red Devils.
Anderson has struggled to hold down a place in the starting XI at Old Trafford, playing just 10 games in the last two seasons and failing to break into Louis van Gaal's side this year.
It had emerged that talks with Internacional had progressed well after the Brazilian flew back to his homeland to complete a medical on Sunday and now a deal has been completed.
However Goal understands United will have to pay a six-figure fee to compensate a loss in wages as Anderson returns to the Brazilian top-flight.
He began his career at Gremio, moving to Porto as an 18-year-old in 2006, before United paid over €30 million for the 2008 Golden Boy winner.
