Since joining United in 2019 he has played 88 games, scoring 22 goals. Ndiaye was a major cog in last season's promotion campaign in which he made 52 appearances in all competitions, scoring 15 goals and providing 13 assists.
United said they "reluctantly accepted" Marseille's offer and had wanted the player, who had one year left on his deal, to stay and help the team in the top flight.
"The Blades offered Ndiaye, 23, a lucrative new contract but unfortunately the club was forced to negotiate with the French Ligue 1 side after the player himself expressed his desire to join his boyhood team," United said in a statement.
The French-born Ndiaye began his career in Marseille's youth ranks in the 2011-2012 season.
He decided to represent Senegal and made his international debut in 2022. Ndiaye, who has seven caps, went to the Qatar 2022 World Cup where Senegal lost to England in the last 16.
