The 22-year-old recently spent a month with Cheltenham Town, scoring twice in seven appearances for the Robins before heading back to The Valley.
Seagulls boss Micky Adams told the club's official website: "Stuart is someone we have tracked for a while.
"He has a decent record when it comes to goalscoring at all the levels he has played at and his one main asset is his pace."
Fleetwood joined the Addicks in the summer from Forest Green Rovers, having scored 36 goals in 50 appearances for the Conference club last season.