Former High Court judge Virginia Bell was asked by Anthony Albanese on August 26 to inquire into the issue after the solicitor-general found Mr Morrison's action had "fundamentally undermined" the principles of responsible government.
Mr Albanese asked for the inquiry to explore how and why the action was taken and who knew about it.
The solicitor-general found it was "impossible for the parliament to hold ministers to account for the administration of departments if it does not know which ministers are responsible for which departments".
Mr Morrison appointed himself to administer the departments of health; finance; industry, science, energy and resources; treasury; and home affairs.
Ms Bell was also asked to look at the implications arising from the appointments for the functioning of departments, and for accountability and public confidence in government.
She will make recommendations to the government on any changes which could provide greater transparency and accountability.
The government has pledged to start work on implementing any recommendations as early as next week.
Former Liberal prime ministers John Howard, Tony Abbott and Malcolm Turnbull have all expressed concerns about Mr Morrison's action.
Mr Abbott described it as "highly unconventional, highly unorthodox" and said it "shouldn't have happened".
Mr Morrison updated his parliamentary biography earlier in November to include the ministries.
The health and finance portfolio roles began in March 2020, while he started as industry minister in April 2021, and home affairs and treasury in May 2021.
He justified the action saying the only time he used his extra powers was in vetoing the PEP11 resource exploration project off the NSW coast.
Mr Morrison intended the powers to be used in only in extreme circumstances "due to incapacity or in the national interest".
They had not been made public because there was no consistent process for publication, he said, but in any case the authorities were legally valid.
"I can only state that I took the decisions I did as prime minister with the best of intentions to do all I could to protect Australia in the face of multiple crises," he said in a statement in August.
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