He looks certain to be named in Australia's squad for the World Cup in West Indies and the United States
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.