A great run of form saw the side leave the bottom three places in the final month of the season.
"It's been one of the hardest decisions I've ever had to make and not one I've taken lightly. Telford means an awful lot to me and it's been a privilege to lead the club this season," Edwards told the club's website.
"It's been a difficult year, I took the job at short notice on the eve of the new season and it took longer than hoped to make the changes I felt were necessary.
"I genuinely feel we showed with our form in the last few months we had turned the corner and I truly believe I'm leaving the club in a stronger position than when I arrived.
It's a decision I have made for me and my family as I still have strong ambitions to progress in my coaching career.
I'd like to thank the fans, the players, my staff and everyone at the club for all their help and support and wish them all the very best for the future."