The 22-year-old will join the 'Cottagers' once the Premier League process the signing.
According to 'Sky Sports', Slavisa Jokanovic's side agreed a fee of £22.3m for the Cameroon international.
Fulham have already completed deals for two players on Deadline Day, bringing in Sevilla goalkeeper Sergio Rico and Atletico Madrid striker Luciano Vietto on loan, and hope to complete the signing of Manchester United's Tim Fosu-Mensah, also on a temporary basis.
Anguissa helped Marseille reach the final of the Europa League last season and also made 37 appearances in Ligue 1 for the French side.