"I'd like to thank Sydney FC for their help and support in my development over the last five years and I will be forever grateful for the opportunity they have given me," Antonis said.
"I'm sad to be leaving such a great club who have been like a family to me as I have grown up and they will always hold a special place in my heart.
"I will continue to support the club and believe they will go on to have a fantastic season with the talent they have in the squad. I wish them well as I embark on a new challenge."
Antonis, 21, made 69 appearances for the Sky Blues in a five-year spell at the club, culminating in a grand final appearance last season against eventual champions Melbourne Victory.
He flew to Europe earlier this week to complete a medical and sign personal terms with PAOK.
Sydney FC coach Graham Arnold wished Antonis well as the Australia midfielder prepares to continue his career overseas.
"Terry has been a great servant to the club and is a great kid with lots of potential. This is a very good opportunity for him and we couldn't stand in his way," Arnold said.
"He has always been keen to make the step overseas and I've no doubt he'll go on to have a long career in Europe, and with the Australian national teams.
"I'm proud of the fact he is another youngster this club has helped to develop and he is another example of the importance Sydney FC and I put into youth development.
"I think if there are any young players who are wishing to further their careers, then they've got a great chance if they come to Sydney FC.
"I'll always look to give youngsters a go and I'm looking forward to producing a lot more young Australian footballers here at Sydney FC."
PAOK, based in the northern city of Thessaloniki, finished third in the Greek Super League last season and will play in the Europa League this campaign.
Antonis, who has Greek heritage and holds a Greek passport, may be loaned out to fellow Super League side Veria FC for his first campaign in Greece, according to reports.