The 23-year-old has followed Nuno Tavares and Albert Sambi Lokonga to the Emirates during a busy summer of spending for the Gunners and is understood to have penned a five-year deal with the North London club.
"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.
Manager Mikel Arteta added: "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 - who previously played a key role in Leeds United's triumphant 2019-20 Championship campaign - will wear the number '4' at the Emirates Stadium, and he will link up with the team ahead of their Mind Series opener with Chelsea on Sunday. body check tags ::