The 28-year old goalkeeper has penned a three-year deal with the Seagulls for an undisclosed fee after spending the past six seasons at Craven Cottage.
Leeds-born Stockdale, who made a total of 52 appearances for the west Londoners, is now expected to play a key role at the Amex Stadium.
"We are delighted to have completed David's signing from Fulham, and I am pleased to welcome him to the club," Seagulls boss Sami Hyypia told the club's official website.
"It is a transfer we have been working on for some time - and David is a goalkeeper with excellent pedigree. He has got very good experience of the Premier League and Championship, but at 28 is in his prime."
Fulham Football Club (@FulhamFC) July 28, 2014
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