Computer algorithms for the scheme wrongly calculated that hundreds of thousands of Australians owed money and with little to no human oversight it recovered US$1.17 billion.

Morrison, who lost power in a general election in May, secretly accumulated five ministerial roles during the pandemic: health, finance, treasury, resources and home affairs.

Virginia Bell will head the inquiry into Morrison's dual appointments to a range of departments, from health and finances to treasury and home affairs, and report by Nov 25, Prime Minister Anthony Albanese says.

Morrison says he did not make the arrangements public because they were a safeguard only and the ministerial powers for health and finance were not triggered.