New Cottagers boss Martin Jol had promised Somogyi he would sign him after the keeper impressed on trial at the manager's former club Ajax last December.
And after passing a medical at Craven Cottage, the 26-year-old Hungarian has put pen to paper on a contract with the Premier League club.
He told origo.hu: "I arrived home in Hungary on Thursday evening and everything had gone well in England so I signed a one-year long contract with Fulham.
"I attended two training sessions during my eight days at the club and on the last two days I underwent a medical, and I'm happy to say that I passed it.
"I'll go back on Sunday and continue the pre-season with my new team."
Somogyi will provide back-up to regular number one Mark Schwarzer, while reserve keeper David Stockdale has been linked with loan moves to Leeds and Swansea.