The 39-year-old, who spent 19 years at Juventus, scoring 208 goals in 513 appearances, failed to agree an extension to his contract.
Del Piero, the biggest signing in Australia's domestic league history, has played a major role in increasing attendances, television audiences and media interest in the A-League.
"At the time, if you had said Del Piero would be playing in Australia, few people would have believed it possible. His signing was the biggest in Australian football history and it lifted Sydney FC and the A-League on to the world stage.
"Together we have achieved a lot and Sydney FC has grown in every way, with record crowds and memberships and huge interest in our club both domestically and internationally."
"Today is bittersweet. While we would have liked to see Alessandro remain at Sydney, his decision now allows us to further our discussions about some exciting new opportunities for our ongoing relationship and to build on the legacy that has been started," Barlow added.
"On behalf of everyone at Sydney FC I would like to say thank you to Alessandro for the enormous contribution he has made to our club over the last two years. It has been a pleasure and a privilege to have him at our club and we look forward to seeing him in the near future when he is next back in Sydney."
Del Piero wrote on his website: "My adventure with Sydney FC is about to be concluded, and, even if it makes me rather sad, because I have had wonderful time here, I have communicated my decision to the club.
"I'm really grateful for the last two years and for the club's request for me to remain and with whom, I am happy to explore new opportunities to continue our relationship. It hasn't been an easy choice, also because my life on and off the pitch has been fantastic, my family and I have really enjoyed these two wonderful years: Australia will remain in our hearts forever.
"My greatest satisfaction is the rapid growth of the Australian football movement, with interest increasing incredibly for the public, television and sponsors, in this country, considered to be an undisputed role model in the world of sportive culture (both for athletes and spectators), the passion for this sport , that I love so much, is constantly growing.
"I will remain a bit 'Australian', and will continue to be close to the football movement in this country and the Australian Football Federation, also as ambassador of the 2015 AFC Asian Cup, that will take place right here next year. See ya mates."
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