Parker's departure announcement came on Thursday and after relegation was confirmed last week following a 1-0 defeat to Manchester City. Burnley said the decision was mutual.
Having gone down in the 2021-22 and 2023-24 campaigns as well, the Clarets will join bottom side Wolverhampton Wanderers in the second-tier Championship next season.
"Following confirmation of the club's relegation from the Premier League last week, Parker and the board held discussions and mutually agreed that his time at Turf Moor would conclude," the club said in a statement.
"He leaves with the respect and gratitude of everyone connected with Burnley Football Club."
Parker led Burnley to the Premier League last season with an unbeaten run of 33 matches after replacing former manager Vincent Kompany. He was previously in charge of Fulham, Bournemouth and Club Brugges.
"It has been an immense privilege to lead this great club over the past two years," former England international Parker said.
"I have enjoyed every moment of our journey together, but feel that now is the right time for both parties to move in a different direction.
"I reflect back with great pride on what we achieved during my time at the club, especially our unforgettable promotion season in 2024-25."
Burnley have begun looking for a new coach and assistant Mike Jackson would be interim for the last four games in the league.
They are second-last in the 20-team division, having won four and lost 22 games, and were eliminated from the FA Cup by third-tier Mansfield Town in February.
Burnley play at Leeds United on Friday before wrapping up the season with games against Aston Villa, Arsenal and Wolves.
With Reuters.
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