Potter joined the Seagulls on a four-year contract in May, replacing Chris Hughton in the role.
The 44-year-old has impressed the Brighton hierarchy with his attacking style of play which has seen them rise to 12th on the Premier League table after 13 games.
Brighton’s bright start has seen them pose victories over Tottenham Hotspurs and Everton this season.
Potter told Brighton’s website: “I’ve had a tremendous welcome from everyone connected to the club — staff, players and fans — and have found it very easy to settle.
“The infrastructure, support and everything associated with the club is first class, and I’m pleased with what we have been able to do already, but there is still a way for us to go.
“I’m thrilled that the club have liked what they’ve seen so far, in a relatively short period of time, and have already shown an added confidence in what we are trying to do.
“I hope that this is just the start of what will be another successful period in our history, and I’m extremely grateful that the club have made this long-term commitment.”
The club’s chairman and owner Tony Bloom added: “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.
“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.”
