The Zimbabwe Cricket Union (ZCU) reportedly took the decision, due to be announced formally later, after it became apparent the International Cricket Council (ICC) would strip the tour of its Test status.

However, the Australian team will stay on in Zimbabwe and play three one-day internationals there.

Former Australian vice-captain Ian Healy praised the decision to call off the Test matches, saying the ICC should be praised for transforming itself from a toothless governing body into one with bite.

"This is the right thing to do," Healy told Australian Associated Press on Friday.

"The ICC was going to vote this way anyway which I think is a strong move from a governing body which is growing in status ... They are looking after the good of the game."

Former England captain Tony Greig said the ZCU had made a sensible but belated decision in calling off the Test series but he hoped the Australians did not catch the first flights out of Harare.

South Africa-born Greig, now a television commentator living in Sydney, said it would be the "worst possible thing" if stars like Shane Warne returned to highly-paid jobs with English county sides when their presence could help Zimbabwe's struggling young players.

"Their threat to come straight home shouldn't be implemented," Greig told AAP.

"Australian cricketers have a responsibility to make sure Zimbabwe cricket doesn't disappear off the face of the earth.

"If they really do care about Zimbabwe cricket, as they say they do, they should take time out to stay there and see what they can do to help these younger cricketers get the idea of what the big time's all about."