Sanchez left Inter Milan after his contract was cancelled by mutual consent on Monday. Chile's most capped player and all-time top scorer has also played for Barcelona, Arsenal and Manchester United.
He made 109 appearances and scored 20 goals in all competitions for Inter after joining from United in 2019 but rarely appeared in the starting lineup last season and struggled for consistent form.
Marseille finished second in Ligue 1 last term and qualified for the Champions League.