The midfielder joined United for ??26m in 2007, but leaves Old Trafford on a free transfer after falling out of favour at Old Trafford in recent years.
Anderson won four Premier League titles, the Champions League, two League Cups and the FIFA Club World Cup in an eight seasons with United.
He was a regular starter in his first four years under Sir Alex Ferguson but a combination of serious injuries – and struggles with his weight – reduced his playing time.
The former Porto player was loaned to Fiorentina last season and United were keen to get the midfielder, who made only 70 Premier League starts, off their books last summer.
No offers came in for the player, though, and he remained at Old Trafford.
Anderson made just one start under Louis van Gaal – in the embarrassing Capital
One Cup defeat to MK Dons at the start of the season.
His only other appearance was a 20-minute cameo at Burnley.
A statement on Internacional’s website confirmed the transfer: “Sport Club Internacional concluded on Tuesday the procedures to announce the signing of midfielder Anderson. He signs a four-year contract.”