Giannou arrives in Cyprus after a rather uneventful two-year spell with Chinese Super League side Guangzhou R&F, netting just two goals in seven league appearances last season.
With first-team opportunities hard to come by, and an eye on making Bert van Marwijk's Socceroos squad for the 2018 FIFA World Cup, the 28-year-old's decision to move back to Europe could be pivotal in his chances.
"I want to thank the family of AEK who gave me the opportunity to come here," Giannou told Larnaca's website.
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"AEK is a very organised club, so I decided to come. It is a team that has challenged for the championship in recent years and that's why I have come to win the championship.
"My goal is to always look higher and with this reason I have come to a team that challenges for the championship to help them as much as I can.
"I had other options, but I thought the best option was to come to AEK, having talked with the team's management about their ambition."
Giannou had been linked with a move to the Central Coast Mariners, with owner Mike Charlesworth admitting the club had been doing everything they could to bring him in as a replacement for the recently released Asdrubal.
The Greek-born Australian has five caps to his name but is yet to score a goal, with his last appearance coming against Japan in 2016.
