The 26-year-old revealed last week that he had spent time on trial with the Cottagers and had been offered a permanent deal.
Fulham boss Martin Jol opted to bring Somogyi over to England after being impressed with him during his time in charge at Ajax.
He becomes the Dutchman's first signing of the summer and will add to the impressive keeping ranks at Craven Cottage.
Somogyi previously turned out for Hungarian side Rakospalotai EAC and arrives in the Premier League eager to make his mark in a major European league.
Confirming the signing on the club's official website, a statement from Fulham read: "Following a successful trial period at Fulham last week, the six-foot-three inch keeper put pen-to-paper on a deal as a free agent with Fulham on Monday morning.
"The club has the option to extend Somogyi's deal at the Cottage by a further year until 2013."