Ginn won the men's coxless fours at the Atlanta 1996 Summer Olympics as part of Australia's Oarsome Foursome, along with Mike McKay, James Tomkins, and Nicholas Green; Ginn replaced the retired Andrew Cooper. Ginn and James Tomkins had planned to race the straight pair at the Sydney 2000 Summer Olympics, but Ginn suffered a severe back injury, forcing him to withdraw from the boat.
In 2002, he returned to the water, teaming up with fellow Oarsome Foursome rower James Tomkins in the coxless pairs; they finished fourth in the 2002 World Championships. In 2003, Ginn and Tomkins were the surprise winners, beating the British favourites—and defending champions—Matthew Pinsent and James Cracknell, which was a factor in Pinsent and Cracknell choosing to move to the coxless fours. At the 2004 Summer Olympics, Ginn and Tomkins won the gold medal in the coxless pairs.
In 2006, Ginn made a return to international competition at the World Rowing Championships held at Dorney Lake, Eton. He and new pairs partner Duncan Free were able to win despite choppy tail conditions.
Scotch College, Melbourne, Ginn's former school, named a racing eight "Drew Ginn" in his honor. The school's first VIII won the APS Head of the River (Australia) in that boat in 1998.
In 2007, Drew Ginn and Duncan Free successfully defended their coxless pairs title, posting a time of 6:24.87 minutes—almost 6 seconds ahead of their New Zealand rivals (Nathan Twaddle and George Bridgewater) who had stuck with them for the first 1000 m before dropping behind to take the silver.
Early in 2008 Drew Ginn and 2007 World Championships gold medal winning partner Duncan Free, were pre-selected to compete for Australia at the 2008 Beijing Olympic Games where they won the gold medal.
At the 2012 London Olympics, Ginn won a silver medal in the Australian men's coxless four, behind the all-conquering Great Britain men's four, who went on to win for the 4th consecutive Olympics.
In 2010 Ginn was inducted as a member of the Rowing Victoria Hall of Fame.
In 2009 Ginn took up competitive road bicycle racing, with immediate success, particularly in the discipline of the time trial.
Ginn won the 2009 Oceania time trial championships. However, in downplaying the achievement, Ginn noted two riders in the under-23 competition actually posted faster times over the same course on the same day.
In a much stronger field at the 2010 Australian national road championships, Ginn finished sixth.