The Bulgarian midfielder was diagnosed with the condition in March last year and is now in remission. In a statement released by Aston Villa, the 33-year said: "It is with a heavy heart that I am announcing my retirement from the game."
Petrov, who joined Villa from Celtic in 2006, is continuing to receive treatment.
His popularity at the club has been evident all season with fans applauding throughout the 19th minute of games - in reference to his squad number - in tribute.
He said: "I've never been a person for making grand statements.
"I've only ever got on with my job, while remaining grateful to have great team-mates, great people around me and, most of all, a fantastic family.
"They have been powerful pillars of support when I have needed them most over the past year. To my wife, Paulina, and my sons, Kristiyan and Stiliyan, I love you very much and I will always for your constant love and support.
"Also to my mum and dad, my brother and Paulina's mum and the people who have been closest to me throughout this time - you know who you are and I love you all.
"Each and every day I thank God for giving me the opportunity to still be with my family. Football has been the other great love of my life, so it is with a heavy heart that I am announcing my retirement from the game.
"The emotions are overwhelming really, but the continued support of family, friends and the great people I have come to know will make it easier for me to move on from the only life I've ever known."
Tributes poured in for the fans' favourite, with former Celtic team-mate and Villa manager Paul Lambert describing his friend as a "fantastic player" and "a nice guy with a heart of gold".
Petrov's priority will now be his health and work for his leukaemia charity, but Lambert revealed he is already mulling over a role for the popular captain. "He'll be missed here but the door will always be open for him," said the Scot.
"I have some things in my head which I'm running over. I've something in my head I'm thinking about at the minute and it's not a sentimental thing at all. It's just some things my staff and myself spoke about, they know what I think."
Petrov will lead Villa out for their traditional lap of appreciation after Saturday's final home game against Chelsea.
"For him to lead out the team will be a great occasion," said the Villa boss. "I think it will be pretty emotional for him when he does it on Saturday."
Lambert added: "Not having him around here during his illness has been a huge blow, it can never be underestimated.
"Him not playing has been massive for this club. Having to try to replace someone like that - a footballer who is a fantastic player - has been hard.
"He has a heart of gold, he's nice guy. I knew him since he was 19 years of age and he first came to Glasgow and I had a good friendship with him. I played with him for nine years and he was always someone you knew you needed to be in the trenches with you."