White spent last season on loan at Leeds United, where he played in all 46 championship games to help Marcelo Bielsa’s men gain promotion to the Premier League after a 16-year hiatus.
Leeds were interested in striking a deal with Brighton to keep White at Elland Road permanently but all efforts were rebuffed for the 22-year-old.
Brighton rejected three bids from Leeds for White, including a £25m offer last month.
Leeds have turned their attentions to Freiburg defender Robin Koch, signing the Germany international on a four-year deal.
White has now committed his long-term future to Brighton, much to the delight of manager Graham Potter.
"I have been looking forward to working with Ben for a long time. He was a player I was well aware of, even before I came to the club," Potter told Brighton's official website.
"He has gradually stepped up the EFL divisions, with Newport County, Peterborough United and Leeds United.
"He had a brilliant season helping Leeds to the title last season, and now he has the opportunity to show his qualities in the Premier League.
"We are delighted to have agreed a new long-term contract with him, and I am sure our supporters will be looking forward to watching him play for the club."
Brighton will host Chelsea on the opening weekend of the Premier League season on September 14.
