Wild, whose side were dumped out of the Vanarama National League play-offs after defeat to Chesterfield on Tuesday night, had been in charge of the Shaman since 2019.
This season he led the club to their highest league finish in 16 years.
In a lengthy open letter to the fans, Wild said: "It is with a heavy heart that I have left the club today. This has been a massively tough decision for me and my family as in the words of my mother, this is a family club.
"In any role in life, you have to leave a job in a better place than you found it and I can safely say I feel this is the case.
"There is a famous quote out there that says, plant trees you may never see grow, I truly hope this is the case.
"This decision has nothing to do with the clubs ambition as they have tried everything in their power to keep me in the building."