Arsenal boss Mikel Arteta said of the signing: "Ben was a top target for us and it's great that we've completed his signing. Ben has been educated with two very good clubs, Brighton and Leeds, in recent seasons.
"He has benefited well from two very good coaching set-ups and has shown with both Brighton and on loan with Leeds what a strong talent he is. Ben is an intelligent defender who is very comfortable with the ball at his feet and his style fits perfectly with us.
"And of course, he is still young, so his age and profile fits with what we are building here. We are all looking forward to Ben being central to our future long-term plans."
White had signed a four-year deal with Brighton last summer after first joining the side in 2016.
Arsenal's technical director Edu added: "Ben has been a key target this summer. He has so many qualities which make us so excited he's joining us. Ben's a young English player with a great future. He's very strong defensively, good on the ball with a great passing range. We're delighted Ben's signed and we look forward to him growing with us."
Sorry we're late...— Arsenal (@Arsenal) July 30, 2021
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He was part of Gareth Southgate's 33-man provisional side and made his debut in warm-up games against Austria and Romania.