The 20-year-old joined Elie Baup's Les Phoceens on transfer deadline day having moved for an initial £4m from Lorient.
Lemina, who only made his professional debut in January, is thrilled to have made the move to Marseille.
"I am living a dream," Lemina told Marseille's official TV station. "I knew that Olympique Marseille had been following me for a while but I had no new information on them recently.
"I only found out at the last minute that OM had made an offer to my club, and I had no hesitation. I have only really been a professional for eight months and it is true that I have progressed quickly. I hope it continues like that.
"My objective for this season is to make major progress by working with players like Alaixys Romao, [Andre-Pierre] Gignac, [Mathieu] Valbuena, who are full internationals. I think I still have a lot of room for improvement, and hopefully I can make a few appearances in the first team too."
Lemina was part of the French side that won the U20 World Cup.