Edwards has been in charge of the Glory on an interim basis since Ian Ferguson's sacking last month, and is expected to sign on for a three-year deal.
The club has announced a press conference for 1pm (4pm AEDT) on Thursday to announce the appointment.
Edwards is expected to stand down from his roles as coach of Australia's under-17s side and his role as an assistant national technical director.
Perth have recorded three wins from five games under Edwards to be within striking distance of a finals berth.
With two rounds remaining, Glory are three points adrift of sixth place and are targeting wins against Melbourne Victory and Adelaide United.
Edwards is renowned for his ability of developing 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."