White, who was a late call-up to Gareth Southgate’s England Euro 2020 squad, has signed a five-year deal, with the option of a further year.
Arsenal saw two bids for the 23-year-old rejected before an agreement was reached with Brighton, who have inserted a sell-on clause.
White is the club’s third first-team summer signing, after left-back Nuno Tavares joined from Benfica for around £8m and midfielder Albert Sambi Lokonga arrived from Anderlecht.
The centre-back made 39 appearances for Brighton in all competitions last season as the Seagulls finished 16th in the Premier League under Graham Potter.
Prior to his debut season in the Premier League last year, White impressed on loan during Leeds’ Championship title-winning side in 2019-20 which led Brighton to secure him on a new four-year contract.