The new deal theoretically ties Potter to the South Coast club until the end of the 2024/2025 season.
Potter had initially signed for four years when he took over from Chris Houghton in May.
His assistant Billy Reid, first-team coach Bjorn Hamberg and head of recruitment Kyle Macaulay have penned similar extensions.
A solid start
He had the opportunity to craft his squad over the summer and made five additions, bringing in the likes of Neal Maupay, Adam Webster and Leandro Trossard.
Maupay, the Seagulls' record signing at £19.8million, and he has scored four goals in 13 league appearances so far.
Brighton sit 12th in the table after 13 matches, having picked up 15 points.
New style key
Club chairman Tony Bloom praised Potter for the implementation of a new, exciting brand of attacking football which he feels supporters appreciate.
He also expressed his confidence that the 44-year-old could establish Brighton, who faced a relegation battle last season under Houghton, as a top-half outfit.
"We’ve been really pleased with the start Graham has made as head coach since joining us in the summer, and I’m delighted he and his staff have committed to these new long-term contracts," Bloom said, as quoted by brightonandhovealbion.com.
"Together with his backroom team, he has continued the club’s progress of recent years and brought a different approach with a new style of play, which has been embraced by players and supporters alike.
"In the summer we unveiled a new long-term vision for us to become an established top-ten Premier League club, and we feel even more strongly that Graham as a bright, energetic and innovative head coach, is the right man to lead us there."
Brighton next face perhaps the trickiest top-flight test at this moment in time: a trip to leaders Liverpool.