The Cottagers have also completed a deal for Seri's former Nice team-mate Maxime le Marchand.
The French defender, 28, played 81 times for the club.
The length of his contract has not been announced, while Fulham have the option to extend Seri's deal, which runs to 2022, by a further year.
Seri said: "I'm delighted to be here, it's a new adventure that starts for me and I'm hoping it will all go well.
"It was great to get the move finalised."
Fulham co-owner Tony Khan said: "Jean Michael arrives with Premier League qualities as well as great promise for the future, which is why he has been at the very top of our target list for a long time."