Turnbull is the fourth prime minister - from both the conservative Liberal Party and more leftist Labor Party - to be dumped by his or her own party before serving a full three-year term since this modern trend of leader-swapping began in 2010.
Morrison made brief public comments Saturday before meeting in Canberra, the capital, with farmers battling a severe drought that is affecting Australia's most populous state, New South Wales, in particular.
"Our job.is to ensure that we not only bring our party back together, which has been bruised and battered this week, but that will ensure we bring the Parliament back together, that we can continue to work to ensure that our country stays close together".
Aged Care and Indigenous Health Minister Ken Wyatt, whose personal popularity is key to the Government holding its most marginal WA seat of Hasluck, would have reconsidered his position if Mr Dutton became prime minister, because he boycotted the 2008 apology to the Stolen Generation.
Turnbull was forced out after an internal power struggle within the Liberal Party.
Morrison was the "candidate best able to gather votes from across the ideological divide", according to The Guardian, which notes that Morrison "was also expected to win support from moderates who once would have viewed him with suspicion".
But it also attracted fierce criticism, fuelled by Morrison's refusal to release details of the military operations to turn back boats, sometimes to countries with dodgy human rights records. Australia sends many asylum-seekers coming by boat to detention centers outside of the country.
He defeated Peter Dutton, a hardliner who led a coup against Mr Turnbull, by 45 votes to 40 in a poll of MPs.
Turnbull, a centrist leader who takes credit for Australia legalizing gay marriage, blamed his downfall on a campaign by hard-right lawmakers backed by "powerful voices" in the conservative media. Turnbull did not stand for election in the vote and said he will resign from Parliament "not before too long".
Mr. Turnbull's departure from politics will spark a byelection for his Sydney seat, threatening the government's wafer-thin one-seat Parliamentary majority.
"There was a determined insurgency from a number of people", Turnbull said.
It is not clear who if anyone will take Turnbull's place on an important trip he planned next week to regional neighbors Indonesia, Malaysia, Thailand and Vietnam, which was to end at an annual forum of 18 Pacific island nations on Nauru on September 5.
The Associated Press reports that the "revolving door" of prime ministers is "universally hated by Australians".