The appointment of Mr Hagger comes after NAB announced a restructure of its private banking business on 8 April 2016.
The restructure will see NAB private banking clients referred to JBWere.
NAB chief executive Andrew Thorburn said: "I am delighted to appoint Andrew to this role. His expertise and counsel, including his deep knowledge of this business and the wealth sector, will serve the board well."
For his part, Mr Hagger said he felt "privileged" to move into the chairman's role.
"We know there is real desire for expert wealth management advice amongst high net worth clients, but this market is largely underserviced," Mr Hagger said.
"Our new high net worth wealth business model is designed to meet that need and forge a new way forward for private wealth advice," he said.
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