Del Piero's appointment was confirmed on Wednesday, with the 38-year-old to return to the role he held with Italian giants Juventus FC for 11 seasons.
"This is a great honour for me to be given the captaincy of one of Australia and Asia's biggest clubs," Del Piero, who also captained Italy on several occasions, said.
"It's a very proud moment for me and I will give everything to help the club win the A-League Championship this season.
"I hope supporters get behind the team and all together we can be successful."
Head coach Frank Farina said of Del Piero's appointment: "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."
McFlynn and Brett Emerton have been named vice-captains.
"It has been a huge honour to be captain and I will continue to give my all for this great club," McFlynn said of his demotion.
"It is a privilege to precede one of the most illustrious names in world football and I look forward to working with Ale and giving him my full support."
The Sky Blues will round out preparations for the 2013/14 season with pre-season hit-outs against Brisbane Roar and Perth Glory.
They will then open the season against the Newcastle Jets at Allianz Stadium on Friday 11 October.