Hodge, who rode in the European peloton up until his retirement at the end of 1996, said he did not want his error to hamper the work of Cycling Australia in trying to move the sport on after the scandal.
CA sacked elite men's road co-ordinator Matt White earlier this week after he admitted to using drugs while riding for Armstrong's US. Postal team.
White was named in the United States Anti-Doping Agency's (USADA) dossier on Armstrong, which alleges that the American won his seven Tour de France titles on the back of a highly sophisticated doping scheme.
"During a stage of my career as a professional cyclist I took performance enhancing drugs - a decision I am not proud of," Hodge said in his letter of resignation.
"I am sorry I did it. It was wrong. I apologise unreservedly to CA, my family, friends, colleagues and cycling fans.
"It goes without saying that these are challenging times for cycling," he added. "But I feel more hopeful than ever for the future of a sport I love."