United paid around £26million for Anderson in 2007, but in recent years he has fallen out of favour and the 20-time English champions have agreed to let the 26-year-old leave on a free transfer.
A statement on Internacional's website read: "Sport Club Internacional concluded on Tuesday the procedures to announce the signing of midfielder Anderson
He signs a four-year contract."
Internacional have not paid anything for Anderson, which means United have taken a huge hit on a player Sir Alex Ferguson identified as a possible successor to Paul Scholes when he signed him from Porto seven-and-a-half years ago.
Anderson was a first-team regular for the first four years of his stay at United, but a combination of serious injuries - and struggles with his weight - reduced his playing time.
The former Porto man was loaned to Fiorentina last season and United were keen to get the midfielder 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.
Source : PA
Source: PA