Covic is expected to join the first-team squad in early September.
Covic heads to Perth after being released by his former cub Western Sydney Wanderers.
He was named player of the tournament after the Wanderers snare the AFC Champions League last year.
Covic, who turned 40 last month, said he wasn't ready to step away from football.
"I've got plenty of gas in the tank and I still have a lot to give back to the game," he said.
"I've thought long and hard about this and the opportunity to extend my career ticks off some personal goals. The chance to play for Perth Glory and win something with a different club is exciting and that's what's most appealing to me."
Last November Covic played a crucial role to help the Wanderers win the ACL final against Al-Hilal in front of a hostile crowd in the return in Riyadh.
"Winning the Asian Champions League medal was an amazing feat and it's something that I'll never forget," he said.
"I've made history with the Wanderers but now I want to leave my mark with another A-League club for as long as I can."
Covic will join former Wanderers teammates Jerrad Tyson and Antony Golec in Perth.
Tyson, who also plays between the posts, last month signed a two-year deal with Glory.
Glory coach Kenny Lowe said he was delighted that Covic was moving to Perth.
"It's fantastic for us and for him," he said.
"He gets to play for at least another year and we've got a quality keeper who's played at the highest level, domestically and overseas.
"We've got three good keepers including youngster Jordan Thurtell so I expect all of them to be pushing each other to play."
Covic kicked off his football career with the Marconi Stallions in the National Soccer League in the 1990s which spawned a career abroad, taking him to Greece and Sweden.
He made two appearances for the Socceroos and was part of the team's squad at the 2006 FIFA World Cup in Germany.
