The 38-year-old former Wales international will concentrate on his role as first-team coach from next season.
Edwards made 179 appearances for the Grecians after joining from Blackpool in 2006.
He began his career at Carlisle before moving to Bristol City, Preston and the Seasiders, and memorably scored the winning goal at Wembley to seal City's return to the Football League.
Source: PA
Source: PA