The Northern Ireland international made 33 appearances as the Seagulls won promotion to the Premier League last season.
The 26-year-old, also formerly of Huddersfield and Reading, told Fulham’s official website: “I’m just delighted to be here.
“Having played Fulham the last two seasons, the football they have played, it suits my style and suits the way I like to play football.
“Once I knew of the interest I was desperate to get it done and I am very happy to be here.”
Brighton manager Chris Hughton said: “Ollie made a key contribution towards last season’s success and this is a good move for all three parties involved. It gives Ollie the opportunity to play regular football.
“Fulham are getting an excellent midfield player, and we’ll monitor his progress throughout the season.”