Buckle, who led the Gulls to the League Two play-off final where they lost 1-0 to Stevenage at Old Trafford on Saturday, becomes the permanent successor to Dave Penney after caretaker boss Stuart Campbell was unable to save the club from relegation to the bottom tier.
"I leave Torquay with a heavy heart after four fantastic years, which included three cup finals and reinstating their place back in the Football League," Buckle told Rovers' official website. "The club now has a solid foundation both on and off the pitch, which will serve them well in the coming seasons. I always wanted to leave Torquay on a high and I am blessed that I can do that."
He added: "The chance to become Bristol Rovers manager was far too good an opportunity to turn down. I intend to do everything in my power to take Rovers back where they belong.
"After meeting with (chairman) Nick (Higgs) and the Rovers board, I am in no doubt of the ambitions of the club and believe with everything in place this club has the potential to reach the Championship in the coming years.
"I will be installing a fresh mentality throughout the club that reflects me by bringing in the high standards that I demanded at Torquay, which resulted in great success."
Source: PA
Source: PA