Australia's next Foreign Minister will be Marise Payne, after 20-year Coalition veteran Julie Bishop announced she would be standing down from the role, despite Mr Morrison saying he "would have very much welcomed her continuing role in the ministry".
Despite his being regarded as a divisive politician with little popularity outside his crucial home State of Queensland, mainstream media predicted a Dutton victory.
"Mr Taylor's extensive commercial understanding will be critical in finding solutions to the competing arms of containing prices, maintaining reliable supply and attracting new investment to the energy sector", Roberts said.
A leaked WhatsApp chat between some Liberal members, revealed by the Australian Broadcasting Corporation on Sunday, showed them pushing against voting for Bishop as a tactic to back Morrison, who finally emerged as the victor.
Labour leader Bill Shorten is now regarded as the preferred prime minister, for the first time since February 2015.
She has served on parliamentary committees for Agriculture and Industry, Indigenous Affairs, Infrastructure and Communications, and Northern Australia.
Mr Morrison visited the drought-stricken Outback on Monday in a demonstration that he has turned his focus away from his government's internal drama to the problems of the nation.
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In the messages, Paul Fletcher warns that former Finance Minister Mathias Cormann was helping gather support for Bishop. The challenge had been instigated by home affairs minister Peter Dutton, whom Morrison defeated in a secret ballot.
Payne's post as Defence minister will be filled in by Christopher Pyne. "The circumstances have appalled most Australians but again, I won't labour the point", he told the Monday meeting, Fairfax reported.
Josh Frydenberg was voted in as deputy leader by his colleagues and given the treasury portfolio on Friday.
Prime Minister Morrison last night finalised cabinet appointments, which included the addition of a Population Minister.
Mr Morrison, whom Mr Turnbull described as a loyal treasurer, excluded Mr Abbott from his first cabinet but has offered him a newly-created role of special envoy for indigenous affairs.
The leader in the Australian's Liberal Party has been named as the new Prime Minster, reports said.