"I have handed my resignation to (the club's leading shareholder) Robert Louis-Dreyfus. It's a decision we have made together," president Christophe Bouchet told a news conference.
"I had already asked to go at the start of the season."
Coach Jose Anigo resigned on Tuesday after Marseille's run of one win in seven games.
Marseille have also lost eight successive matches to arch-rivals Paris St Germain -- two of them this season -- which has enraged the club's fans.
The supporters repeatedly called for Bouchet, who had close links with Anigo, to step down.
Marseille sports director Pape Diouf, a contender for the post of president, said of Troussier: "We have had advanced talks. I cannot yet tell you that we struck a deal but I'm confident we'll make it within 48 hours.
"The new coach, who will most probably be Philippe Troussier, will take the reins for next week's Ligue 1 game against Caen."
Dubbed "the white wizard" after his spells as manager of several African countries, Troussier, 49, will need to find some magic to revive the club.
Seventh in Ligue 1, the former European champions sank 2-0
Marseille have only scored 15 goals in as many games this season while new strikers Peguy Luyindula and Habib Bamogo have failed to deliver.
Troussier had been approached by Marseille in 2002 when Bouchet took over the reins but Alain Perrin was chosen instead.
Troussier's main feat as a manager was taking Japan to the quarter-finals of the 2002 World Cup.
The Frenchman had previously coached Ivory Coast, Nigeria, South Africa and Burkina Faso. He was in charge of Qatar for a short while last season.
Troussier will be the 10th Marseille coach since businessman Louis-Dreyfus took control of the club in 1996.
Louis-Dreyfus, the club's leading shareholder, met Marseille mayor Jean-Claude Gaudin on Thursday amid reports he was about to sell his shares.
Diouf firmly denied the reports.
"Louis-Dreyfus has no intention of stepping down. He's behind the club more than ever," he said.
Troussier will join a club often rocked by controversies and scandals.
Earlier in the week a Marseille court said an investigation into questionable transfers between 1997 and 1999 had been completed and a trial was expected to be held in 2005.