During a three-way vote, whoever comes last in the first round will be eliminated with a second round taking place to decide who becomes leader.
Mr Morrison said he wants to reshape the cabinet on merit and is looking to build a "new generation of Liberal leadership" with a focus on promoting talented women. "I'm getting on with my job of delivering good government for the people of Australia, and supporting the Turnbull government in doing that".
Friday's ballot among Liberal Party lawmakers means Australia's sixth change of prime minister in 11 years, prolonging an era of extraordinary political instability.
After days of uncertainty, Australia finally has a new prime minister - their fifth in eight years - following a dramatic leadership battle.
"There was a determined insurgency by a number of people, both in the party room and backed by powerful voices in the media ... to bring down my prime ministership", he told reporters.
Under the Australian system, as in the United Kingdom, the prime minister is not directly elected by voters but is the leader of the party or coalition that can command a majority in parliament.
"Australians will be dumbstruck and so appalled at the conduct of the past week", said Turnbull.
"In one sense I think there would be continuity (in the economic portfolio), in another sense, (he'll be) trying to downgrade or shift any radical action on climate policy", he told AFP.
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The Opposition Leader Bill Shorten expressed his respect for the outgoing prime minister.
Ousted Australian premier Malcolm Turnbull at Parliament House in Canberra, Australia, March 27, 2018.
"Australia. We owe you an apology".
Some also find his politics confusing - he started his career as a moderate in the ruling conservative Liberal Party and morphed into a conservative. "And I look forward to potentially meeting him at any one of those", she said. "I relish it", he said after rising to the country's highest political role.
WA senator Dean Smith said Mr Morrison's rise to the top job would give the Liberal Party a "strong base from which to campaign" in WA at the upcoming Federal poll.
The irony was all the greater with the architects of two of the coalition's most contentious policies - company tax cuts and the NEG - now leading the party.
Turnbull came to power in a party-room coup in September 2015.
Read about how the Australian leadership was turned upside-down as it happened here.
Past year the deeply Christian Morrison attracted more controversy for opposing a bill legalizing same-sex marriage, even though it had strong support from his party.