The long-expected announcement follows weeks of discussions between Marseille officials and the 58-year-old, whose last club was Athletic Bilbao.
Bielsea also led Argentina for a six-year spell from 1998 to 2004.
Marseille announced on their website: "This Tuesday afternoon Marcelo Bielsa has signed his contract to coach at Olympique Marseille.
"The Argentinian coach will leave this evening for Rosario. His return to Marseille is fixed for June 16 for the return to training, at 6pm.
"Marcelo Bielsa, together with his staff, will hold a press conference earlier in the day on June 16 at a time to be confirmed."
Bielsa, 58, steps in after a difficult season for Marseille. The French giants were relishing a Champions League campaign, but European dreams went sour when the team lost all six of their group games.
Elie Baup was sacked as head coach in December and in his place former boss Jose Anigo assumed control on a caretaker basis.
Marseille could not build up momentum to challenge the leading sides in Ligue 1 and finished sixth in the table, missing out on a place in Europe for next season.
Anigo, who moved from his role as sporting director to take charge of the first team, announced in early May he would be leaving the Stade Velodrome club.