Burn arrived at the Seagulls from Wigan Athletic in the summer of 2018, before heading back to the Latics for the first half of last season on loan.
The 27-year-old joined up with Albion in January 2019, going on to make three appearances in the Emirates FA Cup before the end of last season.
Burn has established himself as a regular in Graham Potter’s side this season and had started all 21 Premier League matches of the season before suffering a broken collarbone in the 1-1 draw with Chelsea on New Year’s Day.
Head coach Graham Potter said, “This new contract is a reward for Dan’s consistent and impressive performances so far this season and we’re delighted to be able to keep him here for another three years.
“He became a key part of the team before his injury setback at the start of the year, and we’re looking forward to being able to welcome him back into the squad as soon as possible.”
Burn is expected to be back to full fitness by the beginning of March.