White has made 60 Premier League appearance for Albion since he joined from Bristol City in 2019, scoring four goals.
The centre back is expected to be a key figure for Albion once again this season and will be an important member of Potter's rearguard especially after White's exit.
Head coach Graham Potter said, “Adam has been a really important figure for us on and off the pitch, so I am delighted to see him commit to the project we have here.
“Adam was one of the first players to sign after I joined the club two years ago and I am delighted with his development in that time. He has captained the team on a few occasions which is a real testament to his qualities.
“We’re looking forward now to seeing him continue his fantastic form from last season into the new campaign.”
The 26-year-old began his career with Portsmouth, making 81 appearances before joining Ipswich Town in 2016.
He spent two years at Portman Road before the Robins secured his signature in 2018, where he remained for a year before joining Albion.
His two seasons with Albion have seen him play a key role in Graham Potter’s defence, as well as contributing up the other end with goals against Tottenham Hotspur, Aston Villa, Arsenal and more recently in the 3-2 win over Manchester City at the Amex.
Southampton look set to beat Brighton in the race to sign talented young right back Tino Livramento from Chelsea for £5m. Livramento, 18, was expected to join Brighton, but Southampton now seem to be in the final stages of signing the England youth international on a five-year deal.
Brighton had hoped Livramento whould be similar to the Tariq Lamptey deal who they signed from Chelsea in January 2020.
Like Livramento, Lamptey's path to the first team is blocked by the excellent Reece James. Callum Hudson-Odoi also played at right wing-back last season for the Blues.
Last year Livramento was voted academy player of the year at Chelsea and in doing so followed James, Billy Gilmour and Mason Mount in winning the award, chosen by coaching staff and senior management in the academy.