Edwards recently guided The Green to promotion as League Two champions - but has now left the club in acrimonious fashion.
Relegated Premier League side Watford have been in talks with Edwards over replacing current boss Roy Hodgson when the 74-year-old steps down later this month.
talkSPORT understands the Hornets are set to name Edwards as their new manager this week.
However, it appears Forest Green owner Dale Vince was left in the dark over talks between the 39-year-old Englishman and Watford.
And in confirming Edwards' exit, Forest Green and their owner expressed their disappointment at the manner of his departure.
A statement from the Gloucestershire club read: "FGR confirms the departure of head coach Rob Edwards.
"Rob was a key part of the team that gained promotion to League One this season.
"We're disappointed that our support, loyalty and honesty towards Rob has been repaid in this way - with negotiations taking place behind our backs.
"We had no contact from Watford, from whom we might expect less, but in any event this kind of behaviour gives football a bad name.
"We thank Rob for all his work at FGR - forgive him the manner of his departure and wish him well."
Vince revealed he called Edwards on Tuesday as speculation of talks mounted - and it was only then that he discovered the negotiations.
He told talkSPORT: "Rob is a talented guy and we knew we would lose him one day, we were sure of that. People come and go in football.
"The manner of it is so disappointing. We are very loyal and very honest. To be repaid with a behind the back negotiation, and also because I've been saying to the media over the last week there's nothing in it because Rob would have told me.
"It's very disappointing. I told Rob that and he accepted it and apologised. It is what it is.
"I hear they are claiming to be starting a new era. This isn't a very good way to start that. Deceit is part of a culture that comes from the top.
"Off the pitch as well as on it, Watford are a club that has issues. That's my opinion."