The former Republic of Ireland international has reached a mutual agreement with the Pilgrims to cancel the final year of his three-year contract.
Sheridan expressed a wish to relocate back to the north of England for family reasons.
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 Two promotion contenders.
“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.
“Everyone at Home Park wishes John every success in his future career.
“The search for a new manager to take Argyle into the eagerly-anticipated 2015-16 season has already begun.”