The 38-year-old World Cup winner, who has captained his country several times and helped Juve to five Serie A titles, signed a two-year deal with Sydney in September 2012.
"This is a great honour for me to be given the captaincy of one of Australia and Asia's biggest clubs," Del Piero told footballaustralia.com.
"It's a very proud moment for me and I will give everything to help the club win the Hyundai A-League Championship this season.
"I hope supporters get behind the team and all together we can be successful."
Del Piero will wear the captain's armband for Sydney for the first on October 11, when the Sky Blues take on Newcastle Jets at Allianz Stadium.
Sydney FC Chairman Scott Barlow added: "We are delighted that Alessandro will be our captain for the forthcoming Hyundai A-League season.
"Alessandro brings a wealth of experience to this role having successfully captained one of the world's leading football clubs for more than decade.
"Alessandro is a natural leader both on and off the pitch and he is recognised the world over as one of the great captains of the modern era.
"It is a proud day for this club to be able to name him as our captain."
Sydney coach Frank Farina hailed Del Piero's impact since his arrival at the club.
He said: "Alessandro is a role model in the dressing room and is highly respected amongst the players at the club.
"He has already shown his leadership qualities since being here, helping out the younger players and becoming a major influence within the team."