Barbarouses, who has also had stints in Russia with Vladikavkaz and in Greece with Panathinaikos, scored 14 goals for Melbourne Victory in the recently completed A-League season before declining a contract extension.
The 29-year-old said he was looking forward to a new challenge but accepted that switching between Australia's two most successful clubs, who have both won the A-League title four times, would not sit well with some Victory fans.
"I want to win trophies and I want to be a big part of a big team," he told reporters outside Sydney Opera House on Friday.
"It was a tough decision to leave ... I've had really good success (at Victory). The fans treated me really well. There's going to be some obvious backlash to that but most people will understand and everyone will move on."
Barbarouses, who has played 47 times for his country, scored the controversial winner when Victory won their fourth title last year with a Grand Final goal that might have been ruled out had the VAR not malfunctioned.
"He's very fast, he scores goals," said Sydney coach Steve Corica. "I think he’s going to be very exciting for our fans to watch as well."
The 15th A-League season will start in early October.
(Reporting by Nick Mulvenney, editing by Ian Ransom)
