The 23-year-old, who was part of the Three Lions squad that reached the final of Euro 2020, joins in a deal worth up to £50m.
He has signed what the club have announced as a “long-term” contract.
Boss Mikel Arteta is delighted to get his hands on what he says was one of his main transfer targets this summer.
“Ben was a top target for us and it’s great that we’ve completed his signing,” he said. “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 follows full-back Nuno Tavares and midfielder Albert Sambi Lokonga as summer arrivals at the Emirates and will wear the No 4 shirt.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies