Boss Kevin Blackwell told the club's official website: "This is really good news for us, the pair have become stalwarts at Bramall Lane and will continue to play major roles in the development of the team."
Quinn added: "I am delighted and it has come at a good time with me starting to find my best form.
"It is nice to know where you stand and it is better to be at a club than worrying about the future.
"It seems strange to see all the comings and goings, but I absolutely love it here. To be honest, I couldn't picture myself anywhere else, but things can change rapidly in football."