The League One champions have secured the 21-year old striker for £1million which has doubled their previous record transfer which came when they signed Andy Ritchie from Manchester United back in 1980.
Seagulls boss Gus Poyet said it was not a tough decision to pay the money for a player of Buckley's caliber.
"I watched three or four of Watford's games last season and Will really impressed," he said.
"Our scouts have also been watching him and have also been impressed. That made it a very easy decision.
"He is young, but he knows the division well, and he is a player I am really looking forward to working with and making him one of us."