Mr Malinauskas took the oath of office at Government House on Monday and said he did so with a "genuine sense of humility".
"The gravity and the poignancy of the moment is not lost on me," he said after the ceremony.
"I take this responsibility incredibly seriously. I approach it with a genuine sense of humility.
"But also with a very firm resolve. A resolve to deliver on our policies. A resolve to use the power and authority invested in my government to do good for people."
Susan Close was also sworn in as deputy premier and Stephen Mullighan as treasurer.
Ms Close said she was honoured to be among the first women to hold the role.
"I think it makes a difference to the way, in particular, young women think about their futures and all women think about how politics can be played," she said.
"We've seen a lot of noise, a lot of talk, a lot of debate about the culture of politics in the last few years and it's a very welcome discussion.
"The best response to it is to have greater diversity on the benches and that means in this case to have more and more women."
Mr Malinauskas is yet to reveal other members of his cabinet, though most who served on his frontbench during opposition are expected to retain their roles.
Some changes are possible given the number of new MPs that will swell the caucus ranks, but all are expected to be sworn-in by the end of the week.
With counting continuing Labor looks set to hold at least 26 seats in the 47-seat House of Assembly, and is leading in two others.
One still in doubt is that of outgoing Premier Steven Marshall, who is trailing his Labor opponent Cressida O'Hanlon in Dunstan.
Mr Marshall has indicated he intends to continue to serve as the local member if returned but has stepped down as Liberal leader.
Shortly before Monday's ceremony, he also arrived at Government House to officially tender his resignation.
Mr Marshall said he had spoken with Mr Malinauskas on Sunday to again congratulate him on Labor's victory.
"I hope that we can continue to work together in the best interests of South Australia," he said.
"It's in a very good position at the moment but there's still much work to be done."
The Liberals should retain 14 or 15 seats but are likely to lose a number of ministers from the previous administration, including Deputy Premier Dan van Holst Pellekaan, Transport Minister Corey Wingard, Child Protection Minister Rachel Sanderson and possibly Primary Industries Minister David Basham.
The new parliament is likely to include five independents with Dan Cregan in the Adelaide Hills, Geoff Brock, who shifted to the seat of Stuart in the mid-north, Troy Bell in Mt Gambier and Fraser Ellis in Narungga, which takes in Yorke Peninsula, are all set to be returned.
In Finniss, independent Lou Nicholson leads Mr Basham after the sitting MP was on the wrong end of a 19 per cent swing.
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