The 33-year-old Bulgaria international was diagnosed with the illness in March last year, forcing him to suspend his playing career.
"I've had my hard moments but I've had good moments as well. I'm lucky because some people with this disease will die very quickly," he told the Villa website.
"I'm glad that this hard year is behind me now and I can concentrate on getting back to my life."
Petrov, who has made over 200 appearances for Villa since joining from Celtic in 2006, is now in remission following an intensive chemotherapy programme.
Villa fans continue to show their support for Petrov by applauding throughout the 19th minute of each game in a reference to the Bulgarian's squad number.
"The support from all the fans, the club, the players, has been amazing," he added.
"The 19th minute has been just incredible. It's them showing their appreciation and their support.
"I don't know how I can thank the fans because it's been incredible. Sometimes I joke with friends when they text me saying, 'You've still got that applause in the 19th minute - when are they going to stop?'"