Deschamps guided the 1993 European Cup winners to their first domestic league title in 18 years in 2010 but since his departure in 2012, OM have struggled to match up with the likes of Paris St Germain and Monaco.
OM said Bielsa had agreed a two-year deal as the club looks to beef up their management after Elie Baup and caretaker Jose Anigo failed to inspire the club's players.
"The (two-year) deal will be finalised with an official signature at the end of the league season," OM said in a statement.
Bielsa, who was in charge of Argentina from 1998-2004 and Athletic Bilbao from 2011-13, will take over from Anigo, who took over in a caretaking capacity last December.
"It is going to be a cultural, but also structural, revolution.
"He is a coach who appreciates working with young players."
Marseille finished second in Ligue 1 behind PSG last season and lie sixth this season with three games left.
PSG and Monaco, who are both foreign-owned, have invested massively on transfers and Marseille have been unable to keep up.
Bielsa, 58, also coached Chile from 2007-11.
In 2012 he guided Athletic Bilbao to the finals of the Europa League and King's Cup, losing to Atletico Madrid and Barcelona respectively.
- Sports & Recreation
- Marcelo Bielsa
- Athletic Bilbao