But while he wasn't party to the move and didn't know about it until it was revealed in the media in recent days, it was a matter for the former prime minister.
"Obviously the prime minister had his reasons, his logic for it, but it was not was not a decision that I was a party to or was aware of," Mr Dutton told ABC Radio on Monday.
"It's an issue for the then prime minister, as it is for this prime minister.
"I'm pretty sure that Anthony Albanese doesn't discuss with the whole backbench and the ministry and the caucus who it is that he has appointed to different portfolios."
A report by The Weekend Australian claimed Mr Morrison secretly took on powers to jointly run the health and finance portfolios when the COVID-19 pandemic reached Australia in March 2020.
The former prime minister's unprecedented move was in response to emergency measures under biosecurity laws and ensured he could administer health and finance powers given to former ministers Greg Hunt and Mathias Cormann.
Mr Morrison also later swore himself in as resources minister and used his powers to overturn former minister Keith Pitt's approval of a controversial gas project off the NSW coast, news.com.au reported on Sunday.
Mr Pitt reportedly did not know the former prime minister had joint oversight of his portfolio.
Prime Minister Anthony Albanese is seeking advice over the constitutional legality of Mr Morrison's actions and was due to be briefed by his department after he arrived in Canberra on Monday afternoon.
Mr Albanese said the Australian public deserved an explanation about his predecessor's decision to swear himself in to the roles.
"This is extraordinary and unprecedented," Mr Albanese told reporters in Melbourne on Monday.
He described the appointments as "the sort of tin-pot activity that we would ridicule if it was in a non-democratic country".
Mr Dutton said Mr Morrison did not swear himself as defence minister, which was his former portfolio in the previous coalition government.
A spokesperson for Governor-General David Hurley said he followed processes consistent with the constitution when he appointed Mr Morrison to the additional portfolios.
"It is not uncommon for ministers to be appointed to administer departments other than their portfolio responsibility," the spokesperson said in a statement.
"These appointments do not require a swearing-in ceremony. The governor-general signs an administrative instrument on the advice of the prime minister."
Mr Dutton said the governor-general had acted appropriately.
"He's a person for whom I have the utmost respect, and he's explained his position, his understanding of the law and constitution," he said.
Mr Albanese said what occurred under the Morrison government was contrary to the democratic Westminster system.
"The people of Australia were kept in the dark as to what the ministerial arrangements were - it's completely unacceptable," he said.
"We have a non-presidential system of government in this country, but what we had from Scott Morrison is a centralisation of power, overriding of ministerial decisions and all done in secret."
Sydney University constitutional law expert Anne Twomey said it was "extraordinary".
"It does raise real issues about the ability of the (former) government to function, at least in its last couple of years," she told Sky News.
"It's not normally legally required for you to (disclose) these things but they form part of ... arrangements we have to make our governments operate in a transparent and open way, so there's been a real failure there."
Nationals leader David Littleproud said he didn't know either, adding it was "pretty ordinary".
"If you have a cabinet government, you trust your cabinet."
West Australian Premier Mark McGowan said national cabinet wasn't informed and "I don't understand how you can get sworn in and it not be revealed".
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