The Seagulls have moved to end growing transfer speculation over White, with Leeds, Liverpool and Chelsea all linked with the 22-year old.
White caught the eye on loan at Leeds last season, but Brighton boss Graham Potter wanted to keep him at the AMEX in 2020.
In other Seagulls news, veteran striker Glen Murray has joined Championship side Watford on a season long deal.
And centre back Shane Duffy is expected to join Celtic on a similar deal when he returns from international duty.