Edwards has been in charge of the Glory on an interim basis since Ian Ferguson's sacking last month, and has led the club to three wins from five games.
With two rounds remaining, Glory are three points adrift of sixth place, and are targeting wins against Melbourne Victory and Adelaide United to secure a finals berth.
Edwards, who coached Australia's under-17s side before linking with Perth, is renowned for his ability to develop youth, and has already signed teenagers Danny De Silva, Riley Woodcock and Matthew Davies since his arrival.
De Silva was just 15 years old when he made his A-League debut off the bench three weeks ago.
Edwards played 93 games for the Glory between 1998 and 2004, and said he wants to return the club to its rightful place as the benchmark team in the competition.
"We're the benchmark club of the competition - always have been," Edwards said last week.
"It's the reason why the A-League modelled everything on what Perth Glory used to be.
"The plan we've got in place is to bring that back to Perth Glory."