The 30-year-old had also been linked with Gremio and Palmeiras as well as Blackburn Rovers but he ultimately chose to sign for the Rio de Janeiro-based side.
Ronaldinho, who also played for Paris St Germain and Barcelona in Europe before returning to his native South America, has signed for Flamengo until 2014.
The Flamengo president, Patricia Amorim, told the club's official website: "We are pleased to announce the hiring of Ronaldinho for the next four years.
"I thank the board for the discretion and wisdom throughout the negotiations. This project started from the first day I got the presidency. I thank the legal department to [the head coach Wanderley] Luxemburgo and especially the fans of Flamengo."