Chester have also made their first summer signing, Solihull Moors striker Harry White, 22, who scored 12 goals in 2016-17, scoring in both of the Midlanders' two wins over City.
Shaw, 30, will combine his playing duties with helping boss Jon McCarthy.
Chester have also made an offer to coach Chris Iwelumo to remain.
The club are hopeful that the 38-year-old much-travelled Scot will continue to combine his coaching role with his media work.
On Monday, Chester announced six players would leave but offered deals to Sam Hughes and James Alabi.
The club lost their last six league games of the season to finish two points outside the relegation zone.
Chester midfielder Tom Shaw has been appointed player-assistant manager at the National League side after signing a new contract at Bumpers Lane.