Thompson oversaw some major successes during his nine-and-a-half years at the club including reaching an Irish Cup semi-final in 2014, winning the Intermediate Cup in 2018, and promotion for the first time to the NIFL Championship division in 2019.
Queen's also pulled off a major cup shock in 2020 defeating Linfield in a famous Irish Cup tie at The Dub.
In a statement the club said it had accepted Thompson's resignation "with great regret" and said it would be "eternally grateful" for the outstanding progress both on and off the pitch made under his tenure at the club.
Club chairman Denis Clarke added: "Peter is our 15th manager during the time of my involvement with Queen's and in my opinion the best manager we have ever had. He will not be easily replaced.
"We have had unprecedented success during his tenure reaching an Irish Cup semi-final in 2014, winning the Intermediate Cup in 2018, and promotion for the first time to the NIFL Championship in 2019.
”When we were drawn at home to play Linfield in the Irish Cup in January 2020. Peter assured us that if we played the game at the Dub, we could win it. Not many believed him, but he masterminded a famous, never to be forgotten victory that day.
"Not only is Peter an excellent manager/coach, but he is also an absolute gentleman. He has had the utmost respect from his players.
"He will always be very welcome at the Dub, and we wish him well in the future."
Thompson described his tenure as a "dream come true".
He said: “Being the manager of Queen’s for one day would have been an honour for myself but to hold the responsibility of leading the club for nearly ten years really was a dream come true.
"I have been involved with the club as a player and a manager for 21 years - over half of my life.
"The club has instilled in me values that have helped not only in my personal life but in my professional life as well.
"I have loved every single minute of it, but, like all leaders, they know when it is right time to stand aside and let the next chapter of the club’s history unfold.
"I will miss the people at Queen’s most of all. The people at this club are simply fantastic.
"I hope I have given all Queen’s supporters a few good days and nights out over the 10 years.
"To the players, a simple, thank you, you have been a pleasure to work with. I hope you all continue to enjoy the club as much as I have over the years.
"Thank you to everyone who has helped support me."
Queen's will look to make an appointment this month as the prepare for life in the Premier Intermediate League following their relegation from the Championship.