Edwards will replace Roy Hodgson, who will leave Watford at the end of this season following their relegation from the Premier League to the Championship.
Edwards recently led Forest Green to the League Two title, meaning they will play in League one next season but without the man who helped them gain promotion.
Forest Green have been left with a heavy heart with the way Edwards' departure has been handled.
They claim the 39-year-old entered into negotiations with Watford without their knowledge but the Hornets insist that Edwards had a clause in his contract allowing him the freedom to speak to other clubs.
“Rob was a key part of the team that gained promotion to League One this season,” a Forest Green statement said.
“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.”
Watford responded in a statement by saying: “Rob had a contractual provision allowing him to leave Forest Green Rovers at any time to discuss employment opportunities at other clubs and the Hornets are delighted to confirm our discussions concluded today.”
