The former France international has been in charge at Stade Velodrome since 2009, and led the club to Ligue 1 glory in his first season in the job.
However, OM endured a torrid league campaign last season, managing a 10th place finish, with financial troubles dogging the club.
And Deschamps has admitted that he has been looking for a way out for more than a month, and feels that his exit would work best for both parties.
"You should know that the directors of Marseille have known my position since May 25 after a meeting in Paris," he told Le Phoceen.
"I am someone [who] always behaves well and will always be respectful to the club. I know what it means to me.
"I've taken this decision because it's impossible to work under these conditions. It would have been detrimental for both the clubs and players."