Petrov, who was diagnosed with the illness in March earlier this year, made 28 appearances for the club last season before receiving the devastating news about his condition.
But in light of the recent good news, the 33-year-old has been quick to offer his thanks for the support he has received over the past few months.
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"I'm fine but it's been hard and tough so far but, thankfully, everything is going in the right direction," he told the club's official website.
"I've been looked after really well by the people in the hospital and so far everything is going in the right direction. I'm really grateful to them and I'm grateful to all of the people who have sent messages of support to me. I appreciate all of this very much."
The former Bulgaria international also singled out the efforts of club masseurs Alex Butler and Andy Smith, who recently completed a 400-mile bike ride to raise money for Leukaemia and Lymphoma research.
The campaign, known as 'Pedal for Petrov', saw the two physios team up with former England international Geoff Thomas to cycle from Celtic Park - a former stomping ground for the midfielder - to Villa Park.
It is hoped their efforts will raise somewhere in the region of £250,000 for the charity, and Petrov admitted to being full of admiration for their efforts.
He added: "Alex and Andy have put themselves through a lot of work and hardship to try to raise money for Leukaemia and Lymphoma Research.
"They have worked so hard and they want to cheer me up and they want to show me how much they love me. It is great to see something like that and, of course, it is for a great cause as well.
"I've experienced something that a lot of people don't experience and I know how important this research is because it helps with all the drugs which people need to get better and better more quickly.
"I asked them to cycle to Bulgaria but they said it was too far to go so they decided to cycle from Celtic Park to Villa Park instead!"
If you would like to support the Pedal for Petrov challenge, you can donate via the JustGiving page at: http://www.justgiving.com/pedalforpetrov or text "STAN91 £3" to 70070