Turnbull, a 60-year-old multimillionaire who holds socially moderate views within the conservative Liberal Party, presented his new team to Governor-General Peter Cosgrove at a swearing-in ceremony at Government House in Canberra.
Attorney-General George Brandis, the government's new leader in the Senate, was the first minister to be sworn in. Scott Morrison took oath of the Treasurer's office.
Payne, one of five women in the new cabinet, was sworn in as Australia's first female defence minister. The previous government had two female cabinet ministers.
Christian Porter took his oath for social services minister while south Australian Simon Birmingham was moved into cabinet for the education portfolio.
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Arthur Sinodinos returned to a senior role in government as cabinet secretary Josh Frydenberg swore his oath as resources and energy minister on the Torah.
Turnbull came to power following last week's leadership vote against Tony Abbott.
According to an AAP report, Abbott was not offered a position. "It's not something that Tony would seek either," Turnbull told a TV channel.
"It's horrible. It is a dark, black experience. It's awful. That sense of rejection. I deeply empathise with him. I am one of the few people who actually has a pretty good insight," he told another TV channel about 57-year-old Abbott.
In the hastily-arranged late night party leadership ballot on September 14, Abbott received 44 votes against Turnbull's 54.
Turnbull's victory is reminiscent of the coup former prime minister Julia Gillard staged against Kevin Rudd in 2010 and makes the former communications minister Australia's fifth prime minister in eight years.