The 31-year-old Croatia international has joined on a free transfer, signing a one-year deal. He had been a free agent since his contract with Hamburg recently expired.
He told his new club's official website: "I like the Premier League and it has always been one of my wishes to come here."
He added: "I played with Hamburg against the club two years ago in the Europa League.
"It was very nice to play at Craven Cottage with a fantastic crowd and I have enjoyed a good relationship with every member of the club I have met since.
"I'm very happy to be part of what is happening at Fulham. The club is doing very well and that was why I decided to come here.
"I know the manager well and I know that he is always looking to strengthen his attacking options - and I hope that we can do even better next season."