The 33-year-old, who has been at Newcastle since 2021, made his England debut in March, just days after helping his club to win the League Cup, their first domestic trophy since 1955.
He was named in the England squad for next month's World Cup qualifier against Andorra and the friendly against Senegal by coach Thomas Tuchel on Friday.
"Dan has had an incredible season. He has been a key part of our most memorable moments and has rightly been rewarded with senior international football," Newcastle manager Eddie Howe said in a statement.
Burn, who has started in 36 league games this season, said he would like to end his career at Newcastle if given the chance.
"It's a dream come true to be playing for this club and I'm delighted that I get to keep doing it," he said.