The 26-year-old Payet, who has five caps for France, will sign next week after a medical, Marseille said on their website.
"Thanks to the agreement found [today], OM will count on one of the major players of last Ligue 1 season," they said about a player who scored 12 goals and set up 12 others last season.
The transfer fee, which Marseille did not disclose, could reach 10 million euros, according to media reports.
"I wanted to stay in France. Being at Marseille means playing the Champions League. I also have the 2014 World Cup in mind," Payet told the club's website.
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