Sky Sport News understands the fee is close to £5m for the Spaniard.
The 30 year old told his new club's website: "I'm delighted to be at an historic club like Fulham, the oldest club in London.
"I'm very happy to have the opportunity to be in the Premier League with Fulham.
"Everything is very positive for me and I want to take the opportunity to make the most of this goal of being in the Premier League."
"He is a tremendous player, that we've targeted for some time.
"His scouting profile and his data profile are both strong, and he has exceptional career credentials including Champions League experience, plus he has worked well with our First Team Goalkeeping Coach Jose Sambade Carreira in the past.
"We expect his addition will make us a more complete and competitive football club."