Mr Marshall and the Liberals have stormed to victory in the SA poll, claiming at least 24 seats, enough to govern in their own right.

He will replace Labor's Jay Weatherill to become the state's 46th premier after ending 16 years of Labor rule.

"I give you my commitment that I and every single person of the team will be working diligently, every day, over the next four years so we can build a brighter future for South Australia," he said.

"A better future for South Australia."

With counting to continue on Sunday, the Liberals could yet build on their slim majority, with at least two seats still in doubt.

The party won 37.3 per cent of the primary vote compared with 34 per cent to Labor.

That was well down on the 45 per cent the Liberals won in 2014 but most of what it lost went to Nick Xenophon's SA-BEST candidates and flowed back by way of preferences.

Mr Marshall said it had been "way too long between drinks" for the Liberal Party in South Australia.

"Now, we have been given a wonderful opportunity by the people of South Australia," he told the jubilant party faithful after Mr Weatherill conceded on Saturday night.

"A massive thank you to the people of South Australia who have put their trust, their faith in me and the Liberal team for a new dawn, a new dawn for South Australia."

Australian Associated Press