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Parliament's Speaker Trevor Mallard announced the appointment today.
"Mr Heron is experienced in conducting high-profile inquiries relating to integrity and conduct," Mallard said in a statement.
Heron was appointed in consultation with Bridges.
Mallard announced last week that a Queen's Counsel would be appointed to lead the inquiry into who might have given the information to Newshub ahead of its public release last Thursday.
Heron will engage a forensic IT expert, and Mallard previously said an employment lawyer would also help with the inquiry.
"It is important to ascertain how this breach of trust occurred and to identify whether there is a systemic issue or an individual is responsible, and if so who that person is," Mallard said.
Mallard noted that Heron and Bridges had worked as Crown prosecutors at the same time but in different firms, and that Heron was appointed by former government minister Chris Finlayson as solicitor-general, and Mallard had himself met Heron several times when the latter chaired Drug Free Sport NZ.
Mallard has not put a timeframe on the inquiry for either its start date or its end. He has not yet been able to put a cost to the taxpayer of the inquiry.