The La Liga club have the option to make the 23-year-old’s move permanent next summer.
“Everyone at Fulham would like to wish Andre-Frank all the best for the coming season,” a club statement read.
Middlesbrough have completed the signing of midfielder Marcus Browne from West Ham – their second signing of the summer.
A product of the Hammers youth academy, Browne spent last season on loan at League One Oxford United, scoring nine goals and providing five assists in 44 appearances.
A delighted Jonathon Woodgate said: “Marcus is an exciting, hungry young player who wants to come and play for this football club. He’s just what we need.
“He can play in three different positions and he is quick. I watched a lot of games for Oxford last season and he’s not only the type of player we want here, but he’s also the type we can improve, and he will get better.”