Anthony Edwards made his Olympic debut at the 1996 Olympic Games in Atlanta, the same Games at which lightweight rowing was first contested. Edwards, a Tasmanian and Bruce Hick won the bronze medal in the lightweight coxed pairs, behind Switzerland and Holland. The previous year, the pair had won the same medal at the 1995 World Championships.
At the Sydney 2000 Games, Edwards joined with Simon Burgess, Darren Balmforth and Robert Richards in the lightweight four. Supported by a parochial home crowd, the crew was leading until 50 metres from the end of the race before it was passed by the fast-finishing French crew and thus had to settle for the silver medal. The same Australian crew had finished third and second respectively at the previous two World Championships. Four years later at Athens 2004, Edwards, Burgess, Ben Cureton and Glen Loftus, in the same boat, finished a gallant second behind the powerful Danish crew. In his fourth Olympic Games at Beijing 2008, Edwards was in the lightweight four that finished third in the B final.
He returned for his fifth Olympic Games in London 2012 as a part of men’s lightweight four alongside compatriots Sam Beltz, Ben Cureton and Todd Skipworth. After finishing second in their heat and then third in their semi-final, the Australian team finished less than a second behind bronze medallists Denmark in fourth place. South Africa claimed gold with hosts Great Britain winning the silver medal.