The Shakers legend, who has been in charge full-time since May 2018 after two spells in caretaker charge, has been linked with a move to Devon over the last few weeks.
Assistant Steven Schumacher is also making the move.
Lowe issued a statement to Bury fans via his official Twitter account.
It read: "I would just like to say a big thank you to all the fans that believe in me and my team over the last 10 months.
"It's been one of the best times of my life.
"You deserve a lot of the credit for the support you have shown us, to not only win promotion but the style that we did it in. Thank you.
"However, the time has come for me to say goodbye.
"To all Shakers fans, the staff at the ground and at Carrington, the youth team staff, and finally my players, this has not been an easy decision for me and my family and I leave with a heavy heart.
"I said I would bring the good times back on the pitch, I did, and I hope the club can continue them in the near future.
"All my love, Lowey. UTS."
The news came just 24 hours after it was announced that Nicky Adams had quit the club after a contract offer had been rescinded. The midfielder has now joined Northampton Town.
In a statement, the Shakers said: "Bury Football Club can confirm that Ryan Lowe has left his role as First Team Manager. We can also confirm that Steven Schumacher has departed.
"Ryan has been a great servant to the club, playing for the Shakers over three separate spells and managing the side to Sky Bet League One.
"Steven was a player with the Shakers for three years, scoring 25 goals and played a pivotal role in the club’s promotion.
"Bury Football Club would like to thank Ryan and Steven for the fantastic job they have done. As a club, we are disappointed to lose such great servants but wish them the best of success in their future coaching careers."