England will host South Africa for a three-Test series, with the first match starting at Lord's on August 17 before games at Edgbaston and the Oval.
The Canberra-based former international underwent emergency surgery in Sydney but his family said he suffered a stroke during the procedure.
Chris Cairns, 51, one of the world's top all-rounders in the early 2000s, was transferred to a specialist unit at St Vincent's Hospital after failing to respond to treatment after a serious cardiac problem in Canberra last week.
The 37-year-old hit the winning runs in New Zealand's triumph, easing the pain of defeats in the past two one-day World Cup deciders.
The Black Caps were also lauded for the manner in which they claimed victory, with pundits saying their sporting spirit shone through during a deserved victory in Southampton.
Tim Southee removed both India openers late on Tuesday to give New Zealand hope of an unlikely victory in the World Test Championship final as the showpiece match headed into the reserve sixth day.
This fixture, worth $1.6 million to the winners and $800,000 to the runners-up, represents the culmination of a two-year programme of series to crown a champion team in men's Test cricket, with India and New Zealand topping the qualifying table.
India face New Zealand in the inaugural World Test Championship final on Friday in a match that could have a profound influence on cricket globally.
Friday's final in Southampton comes after two years of Test series to determine the world's top two teams.
New Zealand captain Kane Williamson has told his side they must "start afresh" in next week's second and final Test against England at Edgbaston after some "superb" cricket enabled them to have the better of a drawn series opener at Lord's.
He faced 347 balls, with 22 fours and went to 200 in style when he hooked express fast bowler Mark Wood for the only six of his innings.
The 27-year-old led England's attack with 2-50 on the first day of the two-match series, but his performance was overshadowed as Twitter messages he had posted as a teenager resurfaced.
The match will be New Zealand's first at Lord's since their agonising Super Over loss to England in the 2019 World Cup final, when the scores were level at the end of 50 overs.
The two teams will face off in Southampton, England from June 18 to 22, with June 23 kept as a reserve day only for lost playing time.
With their innings reduced to 10 overs due to bad weather, Bangladesh were all out for 76 with three balls to spare, well short of the 142 target set by New Zealand.
New Zealand made 173 for five off 17.5 overs after losing the toss and batting, before the weather ended their innings prematurely.
The tourists will play a three-match one-day international series against New Zealand opening in Dunedin on Saturday after completing two weeks of COVID-19 quarantine after arriving.
The team's medical manager Dayle Shackel said Williamson had a small tear in his left elbow that had been irritating him for months.
