Turnbull had been under pressure from poor polling, a looming election, and a revolt by conservative Members of Parliament (MPs), BBC News reports.
This in itself marks a shift from her previous position.
Morrison set to work on Saturday building a new Cabinet, although the only confirmed change so far is the appointment of his Liberal Party deputy Josh Frydenberg, the former energy minister, as treasurer. He also supports Australia's reliance on fossil fuels, and has been ambiguous on his stance toward climate change measures.
Gillard was similarly kicked out by Rudd ahead of a 2013 election, meaning that in a dizzying turn of events the prime ministership went from Rudd in 2010 to Gillard and back to Rudd ahead of the 2013 poll won by Abbott.
"I will be meeting with some colleagues today as we pull the ministry together."
"At the very least, the Turnbull government has been an average-to-good government, by most measures, brought down by internal divisions", said John Warhurst, a political scientist at the Australian National University.
Mr. Morrison, 50, won a closed door leadership vote 45-40 to end Mr. Turnbull's troubled time at the nation's helm.
News.com.au has contacted the Foreign Minister's office for comment.
Morrison has been dubbed the "accidental prime minister" because he had no plans to nominate until Thursday, when Turnbull declared he would not recontest his job.
"I'll be leaving the Parliament ... not before too long", he told reporters.
He said once he received that - if it existed - he would call a meeting at noon tomorrow.
Turnbull came to power in a party-room coup in September 2015.
Turnbull also questioned Dutton's eligibility to sit in parliament when he fronted the media at Parliament House at 1pm today after a tense morning and a mass exodus of 13 of ministers.
"Australia deserves so much better", said one Twitter post.
Turnbull's son, Alex Turnbull, a professional investor based in Singapore, hinted at the feelings inside the family toward Murdoch in a tweet that contained a link to a song by the Rolling Stones, "You Can't Always Get What You Want". But his moderate leadership was always under attack from right wingers in his own Liberal Party.
"What began as a minority has, by a process of intimidation, persuaded people that the only way to stop the insurgency is to give in to it".
Turnbull said that threshold has now been met.
"I think his mission is accomplished", Mr Entsch told News Corp.
A prime minister failing to see out his full term should be a rarity, but in Australia it's become the norm, with a culture of parliamentary back-stabbing that has driven disaffected voters into the arms of fringe parties.