Edwards was in the first season of a three-year deal, but his position became untenable following a rift with captain Jacob Burns and a host of the club's other senior players.
Plalyers were unhappy about perceived favouritism towards Edwards' two sons Ryan and Cameron.
Despite the turmoil, Burns is set to remain as skipper.
Glory are expected to name an interim coach by Thursday.
Chief executive Jason Brewer said Edwards would have remained as coach if he had accepted a series of conditions.
Those conditions are understood to include Edwards having to front the board every week to justify his team selections.
"Unfortunately after two days of discussions with the head coach, we weren't able to reach agreement on those measures being implemented," Brewer said.
Brewer denied Edwards' sacking was a case of the tail wagging the dog.
Edwards' two sons appeared at training on Tuesday, and Brewer said there was no indication that either of them would leave.
Brewer denied the sacking of Edwards might result in a rift between his two sons and the rest of the player group.
"Ryan and Cameron are fully supported by the club," Brewer said.
"They are young professionals that have come in and are looking to make a career in football. I don't see the awkwardness in that," Brewer said.
"They were treated just as much the same as any other player in that club.
"They were on the training pitch this evening and they'll be there tomorrow.
"And they're certainly in contention to play against Adelaide on Sunday.
"They know how to behave in these situations and they'll continue to compete for spots in the team."