Burnely were promoted as Championship runners-up, but looked destined to return to the second division from the very start of this season, struggling to handle the step up.
Their relegation was confirmed on April 22nd, when they lost 1-0 to Manchester City, and that ultimately proved to be Parker's final match in charge.
"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.
"The Club would like to place on record its sincere thanks to Scott for his professionalism, dedication and contribution. He leaves with the respect and gratitude of everyone connected with Burnley Football Club."
Parker replaced Vincent Kompany as Burnley manager in the summer of 2024, following the club's relegation to the Championship, and got them back to the top flight at the first time of asking.
While they were beaten to the title by Leeds on goal difference, it was a hugely impressive campaign nonetheless. They lost just twice, went on a 33-match unbeaten run and kept 30 clean sheets, a Championship record.
However, they weren't able to carry that form into the Premier League, winning just one of their first seven matches and enduring a 16-match winless streak from November to February.
"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.
"I would like to thank Alan and the ownership group for their support during my time at the club. My thanks also go to the fantastic and tireless staff behind the scenes and, most importantly, to the players, who have given me everything since the first day I arrived.
"Finally, thank you to the Burnley fans. I wish you all and this great club nothing but the very best for the future."