The Ligue 1 club announced the 25-year-old defender will sign a four-year deal, until June 2019.
Rafael was told he could leave United earlier this summer after being left out of the squad for the club’s pre-season tour of the United States.
A statement on OL’s official website read: “Olympique Lyonnais informs of an agreement with Manchester United for the transfer of Brazilian international Rafael da Silva, who will sign in the coming days a 4-year contract with OL, ie until June 30, 2019.”
Reports in France suggested Lyon will pay up to £2.5million for the signature of the three-time Premier League winner.
Rafael joined United along with his twin brother Fabio from Fluminense in 2008.
Rafael went on to establish himself as a first-team regular under Sir Alex Ferguson and David Moyes, but new manager Louis van Gaal often overlooked the defender, choosing Antonio Valencia ahead of him.
Rafael started just six Premier League games in the 2014-15 season, the last of which came on October 26 against Chelsea.
And when Van Gaal signed right-back Matteo Darmian from Torino this summer, it was clear Rafael was surplus to requirements at Old Trafford.
He becomes Lyon’s third summer signing after forward Claudio Beauvue from Guingamp and defender Jeremy Morel, who was a free transfer from Marseille.
United wrote on Twitter: “#mufc wishes Rafael the best of luck with his new club as he prepares to join Olympique Lyonnais on a four-year deal.”