The 22-year-old joins the Cottagers for a reported fee of £30 million (€33m/$39m) and signs a five-year deal.
"Andre’s tremendous data profile, his glowing scouting reports, and his sterling reputation confirm his world-class talent," said Fulham director of football Tony Khan.
“Throughout this summer, we’ve pursued elite players on whom we believed we could rely to deliver the quality required to challenge the great competition we’ll face in the Premier League, and thus, Andre has been one of our top targets."
Anguissa becomes the fifth deadline-day signing for the Cottagers, after Sergio Rico and Joe Bryan confirmed their moves to the newly-promoted side earlier on Thursday.
The signing wraps up a busy summer for Fulham, with the likes of Jean-Michael Seri, Andre Schurrle, Alfie Mawson, Fabri and Aleksandar Mitrovic also arriving.
Fulham begin their return to the Premier League on Saturday when they take on Crystal Palace.