Rumours emerged last week that Milicevic, who has previously played for Newcastle Jets and Melbourne Victory, was poised to sign with Glory, returning to the club where he made his name in Australia before leaving for Europe in 2001.
Victorian Premier League club Melbourne Knights, where Milicevic has been playing, released a statement on Monday that the 32-year-old former Socceroos defender had left to join Glory and Perth confirmed the signing today.
"Ljubo made contact about 10 days ago and obviously that triggered our interest as he's a quality player and a former champion player of the club," Edwards said.
"I discussed it with (Perth assistant coaches) Gareth (Naven) and Scott (Miller) and we were all unanimous in saying that it would be great to have him back here.
"I believe it's a good fit for Ljubo and a good fit for the club."
Milicevic played for Zurich, Basel, Thun and Young Boys Bern in six years in Switzerland before signing for the Victory in 2007.
After a falling out with Victory head coach Ernie Merrick and captain Kevin Muscat, Milicevic only played two games for them before moving to the Jets.
Milicevic's stint at the Jets also involved plenty of controversy, slamming Newcastle's then-owner Con Constantine for treating the players like 'amateurs' during their 2009 Asian Champions League campaign.
But despite Milicevic's highly-publicised struggles with depression and off-field discipline, Edwards is convinced the veteran, who can play as a central defender and a defensive midfielder, will be focused for Perth.
"He's had his issues down through the years but although we're mindful of those issues, we're not going to dwell on the past," Edwards said.
"We're a forward-thinking club and we are looking at the many positives that he's going to bring to our culture.
"We want him to just concentrate on playing football and assisting us in moving the club forward with all the experience that he can bring.
"The fans of Perth Glory should be excited again because he's a very experienced player who is going to improve us as a club going forward."
Milicevic played 29 games for Glory in the defunct National Soccer League before joining Zurich.