The 23-year-old has signed a five-year contract at the Emirates Stadium with the option to extend for a further year.
White is Arsenal’s third summer signing after Nuno Tavares joined from Benfica and Albert Sambi Lokonga arrived from Anderlecht.
The England international has been handed the number four jersey.
White made 36 Premier League appearances for Brighton last season as the Seagulls finished in 16th position, having spent the previous season on loan at Leeds United, whom he helped gain promotion to the top flight.
Arsenal manager Mikel Arteta said: "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 benefitted 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 has been capped two times by the England national team and was part of the squad at EURO 2020.
