Sheridan and the club have agreed to cancel the final year of his three-year contract with immediate effect.
Argyle made it to the League Two play-offs earlier this month but they were knocked out in the semi-finals by eventual losing finalists Wycombe over two legs.
Argyle owner and chairman James Brent said: “John has made a significant contribution to the Pilgrims’ cause, for which we will always be very grateful.
“Under his management, Argyle were brought back from the brink of relegation out of the Football League and were subsequently transformed into League 2 promotion contenders.
“Reaching the play-offs last season, two years after surviving the drop into non-league on the final day of the 2012-13 campaign, is an achievement of which John, his management team, and the players should rightly be proud.
“While we would have liked John to continue to plot Argyle’s course back up the Football League, we understand his reasons for wanting to leave and have agreed a mutual termination of his contract.”
Sheridan said: “It has been a pleasure and a privilege to have been Plymouth Argyle’s manager for the last two and half years, and I would like to thank the Board and the Green Army for supporting me wholeheartedly during my time at Home Park.
“I have thought long and hard about the decision I have reached and I hope people understand the reasons behind it.
“I believe that I leave the club in a far stronger position to reclaim its place at a higher level of the Football League than it was when I first arrived and I wish it nothing but continued success for the future.”