Morrison - an evangelical Christian known as "ScoMo" - replaced a man who became the latest in a long line of leaders knifed in the back by ambitious colleagues.
The political crisis began on Tuesday when Turnbull called a leadership vote at a regular Liberal Party meeting in an effort to scuttle an obstructive campaign by conservatives that had already destroyed a key energy policy.
Morrison told reporters: "We intend to be governing.so I don't think anybody should be making any plans for any elections any time soon".
The insider view is that a secret ballot is the way to settle the leadership, but the insider view has given Australia seven prime ministerships in a bit more than a decade.
The political uncertainty saw the Australian dollar AUD=D4 down 0.1% on Friday, after falling 1.4% on Thursday, the worst performing major currency on the day.
"It was extraordinary. It was described as madness by many, and I think it's hard to describe it in any other way, " Mr Turnbull said.
"It was described as madness by many, and.in so far as there has been chaos this week, it has been created by the wreckers".
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The disarray has stoked a political realignment in Australia, with a hodgepodge of independents and smaller parties, like the anti-immigration One Nation, stepping into the void to mop up disaffected voters.
Ousted Australian premier Malcolm Turnbull at Parliament House in Canberra, Australia, March 27, 2018.
Turnbull faced opposition from conservative members of his party over low poll numbers as the country approaches a general election in May 2019. New South Wales is Australia's most populous state and the drought is the most severe in recent memory.
"Do you know where Australia is?" one Twitter user wrote back to Trump. MR Morrison said the rest of his Cabinet would be sworn in next week.
Fast-forward to 2015 and Turnbull got his revenge by dramatically forcing Abbott from office in a Liberal Party coup, claiming the government faced defeat at the next election without change at the top.
Morrison has a reputation as a powerbroker within the Liberal Party whose support has been crucial to previous party leaders.
In his first statement after being elected Liberal leader three years ago, Turnbull urged Australians to embrace disruption.
On social issues, Morrison has stood to the right of the more moderate Turnbull, and opposed the legalization of same-sex marriage previous year.