Lemina joined last season's Ligue 1 runners-up on Monday, signing a five-year contract with the club.
He cost Marseille an initial fee of €5million, with add-ons included, while Rafidine Abdullah and Larry Azouni went the other way, the latter on loan.
The move represents a significant breakthrough for Lemina, who only made his professional debut in January this year.
But the 20-year-old – who helped France to victory in the FIFA Under-20 World Cup this year – is highly rated and could prove to be a bargain buy for Marseille going forward.
"I am living a dream," Lemina told Marseille's official TV station.
"I knew that OM (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."
Lemina is hopeful that his meteoric rise will continue and feels he will benefit greatly from training and playing with other members of Marseille's squad.
"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," he said.
"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."
Marseille were one of the busiest Ligue 1 sides on the transfer deadline day, as they also signed Lille star Florian Thauvin.
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