Mr Clyne assumed the chairmanship of Clydesdale two years ago during an overhaul of the bank's board that included the departure of long-standing chairman Sir Malcolm Williamson and which came after the Glasgow bank suffered large property loan losses.
Mr Clyne is to be replaced as NAB chief executive by fellow Australian Andrew Thorburn, who has run the Bank of New Zealand for the group since 2008. But NAB has not yet decided whether Mr Thorburn will assume Mr Clyne's place chairing the Clydesdale Bank board.
David Thorburn, the Clydesdale Bank chief executive, who is not related, said: "I am very grateful to Cameron for his support over the last few years and I look forward to working with both Cameron and Andrew in the coming months."
A Clydesdale spokesman said of the chairmanship: "Cameron Clyne is in his role until the end of August. There are decisions that need to be made between now and then.
"The board will appoint a new chairman and it will be announced to the stock market when it happens."
Andrew Thorburn has some experience of British business having taken a Master of Business Administration at the University of Durham.
It is understood that it was 46 year-old Mr Clyne's decision to leave the bank in August, having been chief executive since 2008.
Mr Clyne said: "I am leaving to spend some much-needed time with my young family. I am proud that I leave NAB as a strong, customer-focused bank."
NAB chairman Michael Chaney said: "Cameron took over as CEO during the global financial crisis and developed an effective strategy to steer the bank through a challenging period during which it has undergone significant cultural and structural change.
"He is highly regarded throughout the bank and externally, and we are sorry to see him leave at this time."
NAB is the largest of Australia's "Big Four" banks by assets, but the smallest by market capitalisation and despite strong earnings and share growth, it has underperformed its rivals during Mr Clyne's tenure.
Some NAB investors blame Clydesdale Bank, which also owns Yorkshire Bank, for putting a brake on performance.
Robert Webb, Associate Professor in Banking at Nottingham University Business School, said banks in Australia avoided many of the excesses of UK banks so were less affected by the financial crisis.
"They (shareholders) look at the performance of the two banks (Clydesdale and Yorkshire) that National Australia Bank has in the UK, look at financial indicators like return on equity and they wonder if owning them is worthwhile," he said.
Clydesdale, which employs around 4,000 people in Scotland, has taken capital injections from its parent to cope with losses on property loans and has retrenched back into its heartlands in Scotland and the north of England under David Thorburn, its chief executive since 2008.
There have been indications that NAB would like to sell Clydesdale or float it on the stock exchange, with Mr Clyne indicating last summer that he would keep an eye on spin-outs such as TSB from Lloyds Banking Group and Williams and Glyn from Royal Bank of Scotland.
Dr Webb dismissed the idea that Clydesdale is too small to compete in the UK banking market.
"There is certainly a place for this bank. Clydesdale has a heritage, it has a customer base, it has a branch network. They are the things that are hard to establish if you are a new entrant," he said. "There is nothing to say that Clydesdale should not be a successful bank in Scotland."
Mr Chaney described Andrew Thorburn as an outstanding banking executive who had been part of the executive team that developed its strategy of focusing on its Australian and New Zealand operations.
"Andrew Thorburn has done a superb job leading Bank of New Zealand since 2008 where he continued to build the bank's performance, increasing cash earnings by more than 40%, improving market share on the back of strong customer satisfaction and developing a strong leadership culture."