The Argentine has been given a two-year contract and will take over from Frenchman Jose Anigo.
The French side were Ligue 1 runners-up last season, but currently sit sixth in the table and are unable to qualify for the Champions League.
"I'm a big fan of Argentine football in general and of Marcelo Bielsa in particular," Marseille president Vincent Labrune told RMC.
"We got in touch with very few coaches. I believe it's a great chance for Marseille to have Marcelo Bielsa with us.
'We hope to turn a corner with Marcelo. It's going to be a cultural revolution but also a structural one. I think it's a necessary step to help Marseille deal with a new economic environment and especially new rivals."
Bielsa has managed Argentina and Chile, with his last role coming at Athletic Bilbao in 2013.