The French side announced the signing of the Brazilian full-back following a medical on Monday.
He had one-year left on his contract at Old Trafford but was told he was not part of manager Louis van Gaal’s first-team plans this season following the arrival of Italian Matteo Darmian.
A statement on Lyon’s 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 four-year contract with OL, ie until June 30, 2019.”
Reports in France suggested the club will pay up to £2.5 million for the three-time Premier League winner.
Rafael, who joined United in 2008 from Fluminense, made just 11 appearances last season.
The defender established himself as a first-team regular under Sir Alex Ferguson and David Moyes, but Van Gaal often overlooked him in favour of Antonio Valencia.
He made 96 Premier League appearances in total for the Red Devils, scoring five goals.
His twin brother Fabio left United in January 2014 to join Cardiff City.