The London outfit have been in the market for a midfielder and previous reports linked Nigel Reo-Coker and Owen Hargreaves with the position.
Despite speculation, Fulham have signed 29-year-old Tavares, who played under Cottagers boss Martin Jol at Hamburg during the 2008-09 season.
"I'm happy that I'm now officially a Fulham player and I'm looking forward to playing under Martin Jol once more," Tavares told the club's official website. "The players and staff have made me feel welcome and I can't wait to get started with my new teammates."
Jol added: "Mickael is a typical holding midfielder and I'm delighted that we've been able to strengthen this area. He played for me when I was at Hamburg so I'm familiar with his qualities and he will prove to be a very good addition."
Tavares has 29 caps under his belt with Senegal.