The Stoke City academy graduate has lined up against the Pilgrims over the course of the last two seasons in Chester FC colours.
The 22-year-old has now put pen-to-paper to become Ian Culverhouse's second new signing since the Pilgrims earned promotion to the National League.
Having made 56 National League North appearances for the Cestrians, Coates will link up with the United squad when they report for pre-season training in July.
Frankie Maguire was unveiled as the club's first summer signing on Saturday.