The former Republic of Ireland international said goodbye to the League Two club on Thursday evening after expressing a wish to return to the north of England.
Sheridan had narrowly failed to guide the Pilgrims to promotion, losing to Wycombe in the play-off semi-final.
The former Sheffield Wednesday star 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.”
Argyle search for a new manager has now begun, with former bosses Neil Warnock and Ian Holloway among the names linked.