Former teammates including Scott McGrory and Phil Bates have paid tribute to Wooldridge on Twitter.
The Australian Minister for Health and Sport Greg Hunt MP has also shared some kind words following the devastating announcement.
"Deeply saddened to hear about the loss of Olympic champion Stephen Wooldridge. My thoughts are with his family and loved ones," he Tweeted.
Cycling NSW has released a formal statement, too.
"Stephen was an inspirational figure in track cycling, particularly in his home state of NSW,” the statement said.
"He was an outstanding team pursuiter, being a four-time world champion in the discipline along with being the 2002 Commonwealth Games champion. Perhaps his greatest feat, occurring at the 2004 Athens Olympics where with his team mates Dawson, Lancaster, Brown, McGee and Roberts, he took gold for Australia.
"Stephen was inducted into the NSW Sports Hall of Fame in 2015; an honour he was delighted to receive both personally and for the sport of cycling.
"Stephen went onto pursue a career in the tertiary education sector primarily with the University of NSW, where he was a prominent administrator. This extended to his various roles with Cycling Australia and Oceania Cycling Confederation Boards and Committees.
"Cycling NSW’s thoughts are with Stephen’s family and his friends during this difficult time.”
Meanwhile, Cycling Australia has not yet to comment or release a statement on the sportsman's tragic passing.