The Bulgarian international, who recently turned 33, said that he was inspired by the messages of support he received while undergoing treatment for the illness.
"I've been a strong character since the start of my career," said Petrov. "I always believed that you need to be patient and you need to believe in things - and I believe that I will get better.
"I know it is hard and I've been through a hard time but the doctors, nurses and everybody in the hospital have been great to me. It has been great because if you have people that you trust it makes it easier and they have made it easier for me.
"I know I've got a few more months of chemotherapy and I need to go through it but I think that the hardest bit is over and from now on I just need to wait for the result to be positive."
Aston Villa's new manager Paul Lambert, who played alongside Petrov at Celtic, recently confirmed that he will remain captain under his tenure.