The 33-year-old Bulgarian international was diagnosed with the illness in March 2012, and after a year out of the game, Petrov has said that he is looking forward to getting back to "a normal life".
"I've had my hard moments but I've had good moments as well," Petrov told the club's official website.
"I'm lucky because some people with this disease will die very quickly. I'm glad that this hard year is behind me now and I can concentrate on getting back to my life.
"I have finished all of the high intensity treatment and from now on I'll be on the softer treatment, which is two years on tablets. It was a very, very long year but now, after all this treatment, I can go back to a normal life."
Petrov, who has made more than 500 career appearances for Celtic and Aston Villa, has hailed the support of the Aston Villa fans as "amazing".
"I don't know how I can thank the fans because it's been incredible. The support from all the fans, the club, the players, has been amazing," he said.
Petrov joined Villa from Celtic in 2006.