Fenerbahce confirmed an agreement was reached with both the player and the French club, with the transfer fee to be paid in three equal instalments over the next three years.
The Istanbul-based side will also cover any solidarity payments arising under FIFA regulations.
Greenwood joined Marseille from Manchester United in July 2024 on a five-year contract after ending his long association with the Premier League club.
Fenerbahce will hope he will add firepower to their frontline as they chase a first Turkish top-flight title since 2014. The versatile forward bagged 37 league goals in 66 appearances over two seasons for the French side.