The 39-year-old striker's two-year contract expired with the club's 2-1 defeat to Melbourne Victory in the A-League elimination play-offs earlier this month.
"Australia, the moment has arrived to say "arrivederci"," Del Piero said in a statement 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.
Super League will 'reshape' after English clubs quit
"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."
Del Piero's arrival in Australia on a A$4 million (£2.2 million) deal in 2012 was hailed as a coup of sorts for the league.
Del Piero, who is also the ambassador for the 2015 Asian Cup in Australia, said he will need some time to decide on his future.
Media reports have been linking him to DC United in the Major League Soccer.
Sydney FC also paid rich tributes to the evergreen Italian.
"Two years ago Sydney FC signed one of the greatest players to have ever worn a football shirt, Alessandro Del Piero," Sydney FC Chairman Scott Barlow said in a statement.
"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 onto 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 bitter-sweet. 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.
All six Premier League clubs withdraw from European Super League
Schalke relegated after loss at Bielefeld