Wooldridge won Olympic gold in the 4000m team pursuit at Athens in 2004, also claiming four world titles in the same discipline during the 2000s.
He was not part of the quartet of Graeme Brown, Brad McGee, Brett Lancaster and Luke Roberts who won the pursuit final in Athens.
But along with Peter Dawson, he was awarded a gold medal due to his participation in the preliminary round.
Cycling NSW confirmed the cyclist's death in a statement.
"Stephen was an inspirational figure in track cycling, particularly in his home state of NSW," the governing body said.
"Cycling NSW's thoughts are with Stephen's family and his friends during this difficult time."
Wooldridge, who also won gold at the 2002 Commonwealth Games in Manchester, is being remembered for his efforts in supporting young cyclists.
Cycling promoter Phil Bates said Wooldridge was Australia's most successful track pursuit cyclist at the time of his retirement.
"In your lifetime, you give support, encouragement and the opportunity for young cyclists to reach their goal," Bates wrote on cycling magazine Ride's website.
"In our sport of cycling, you see some conquer with lesser effort than others. Then you witness those that continue to work harder and reach even greater heights."
Wooldridge was inducted into the NSW Hall of Champions in 2015.
He sat on Cycling Australia's board from 2007 to 2013
"Steve will be remembered by so many for not only his success in competition but also for the contributions he made across so many roles in the sport," CA chief executive Nick Green.
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