Parker took charge of Burnley in July 2024 – signing a three-year contract – and led them back to the Premier League at the first time of asking with a second-place finish in the Championship.
“It has been an immense privilege to lead this great club over the past two years,” said Parker.
“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, and it was a true honour to lead this team into the Premier League.”