The wicketkeeper-batsman missed the previous series against New Zealand owing to a paternity leave
Cairns, 51, initially underwent surgery in Canberra for an aortic dissection before being moved to Sydney for further treatment.
"It's been a big 6 wks. On 4th August I suffered a Type A aortic dissection, a rare but serious condition. I required emergency surgery and from there a range of complications ensued..." Cairns wrote on Twitter on Sunday.
"I ended up suffering a spinal stroke. A long road ahead, but I'm grateful to be here."
Cairns, a former captain of New Zealand's one-day international team, played 215 ODIs and 62 Tests from 1989-2006.