The 22-year-old joined Marseille from Reims in 2015, and leaves the French outfit having made more than 100 appearances over the last three seasons.
Anguissa also represented Marseille in last season's Europa League final, and has seemingly concluded what has been a very busy summer transfer window for the Cottagers.
"I am delighted to have signed for Fulham today. This is a new chapter in my career and one I'm really looking forward to," Anguissa told the club's official website.
"I hope to bring my qualities to this new project. I like a challenge and I will ensure that I give my very best to my team, the club, and the supporters."
Anguissa, who is an 11-time Cameroon international, could make his debut for Fulham in their Premier League opener against Crystal Palace on Saturday afternoon.