Beye, 48, succeeds Roberto De Zerbi after the Italian left the 1993 Champions League winners early last week in the wake of a 5-0 hammering by bitter rivals Paris Saint-Germain.
He takes over a team which lies fourth in France's Ligue 1 with 12 games of the season remaining, five points adrift of Lyon in third and 12 behind leaders Lens.
The top three qualify automatically for next season's Champions League, with fourth entering in the third qualifying round.
Beye will be officially unveiled on Thursday before his first game in charge on Friday, away to Brest.
Former Senegal international full-back Beye had been in charge of Rennes for just over a year having previously been coach of lower-league side Red Star, and he also worked as a prominent pundit on French television.
He played for Marseille from 2003 to 2007, notably featuring alongside Didier Drogba in the team that lost the 2004 UEFA Cup final to Valencia.
He also played for Strasbourg and finished his career in England, turning out for Newcastle United and Aston Villa as well as Doncaster Rovers in the second tier.
"His deep attachment to Olympique de Marseille and his intimate knowledge of the environment in Marseille can be major assets in taking the club to the next step," said a statement released by OM, who did not reveal the length of Beye's contract.
The announcement of Beye's arrival in Marseille came hours after his severance deal with Rennes was finalised and they appointed his successor in the shape of Franck Haise.
Frenchman Haise signed a contract until 2027 after Beye was dismissed with the Breton outfit sitting in sixth place in Ligue 1.
Haise, 54, guided Lens to the Champions League group stage in 2023/24 after the club finished runners-up in Ligue 1 the previous season.
He joined Nice in June 2024 but left in December after just five wins from 16 league games. He returns to Brittany after a six-year stint as a coach in the Rennes academy from 2006 to 12.
"It's a joy to return to Rennes, a true pleasure, with my staff, to join such a great club," Haise said in a statement.