The 23-year-old midfielder becomes the second African to leave the London club this summer, after Jean Michael Seri's temporary switch to Galatasaray.
The Spanish top-flight outfit have the option to make the deal permanent at the end of the season.
He made 22 Premier League appearances for Fulham in the 2018-19 season and he was also part of the Cameroon squad which featured at the 2019 Africa Cup of Nations in Egypt, where they bowed out in the Round of 16.
Good luck at @VillarrealCF, Frank 🤝— Fulham Football Club (@FulhamFC) July 26, 2019
Anguissa is expected to link up with compatriot Karl Toko Ekambi in Javier Calleja's team at their pre-season training base in Austria.