Coppell, 58, is reported to have considered his future with the club after the dismissal of manager Richie Barker on Wednesday, who he had appointed.
Chief Executive Michael Dunford released a statement on the club's official website confirming Copppell's departure.
"Steve will always have a special place in our hearts at Crawley Town FC because he was instrumental in assisting Craig Brewster in securing our promotion to League One and has since been a very good advisor to the both the board of directors and the team management.
"Steve is a long term friend of our owners and will always be welcome at Crawley Town FC and we wish him every success for the future."
The former Crystal Palace and Reading boss has been out of management since a stint with Bristol City in 2010 but has recently been linked with a return, with Barnsley, Sheffield Wednesday and Wigan Athletic all linked with the veteran having parted company with their respective coaches at the weekend.