The 29-year-old Toronto native succeeds Jarome Iginla as team captain. Curtis Glencross and Mike Cammalleri will return as assistant captains.
"Mark represents all the qualities that we set as a coaching staff and an organization," head coach Bob Hartley said in a statement. "He is a quality man who is proud to represent the Calgary Flames both on and off the ice.
"We are very happy with these three men leading and setting the example for our team, and especially our young players, as we move through this crucial yet exciting period in the history of the Flames franchise."
Iginla was team captain for nine seasons before signing with the Boston Bruins as a free agent in the off-season.
Giordano has 150 points (41 goals, 109 assists) and 366 penalty minutes in 385 career regular-season games with the Flames. He has one goal in four career playoff games.
He was invited to attend the team's development camp in the summer of 2004, signed as a free agent and spent the next two seasons with Calgary's American Hockey League affiliate.
He split the 2006-'07 season between the AHL and Calgary before becoming a staple on the Flames' blue-line the following seasons. Giordano was appointed assistant captain to start the 2011-'12 season.