Mr Speirs, who was born in Scotland before moving to Australia with his family as a teenager, won a leadership ballot on Tuesday.
The 37-year-old was selected ahead of other touted candidates Heysen MP Josh Teague and MacKillop MP Nick McBride.
Mr Speirs won the leadership with 18 votes, to Mr Teague's five and Mr McBride's one.
He will become opposition leader as former premier Steven Marshall moves to the backbench after holding on to win his local seat of Dunstan by 0.5 per cent.
Mr Marshall served as leader of the SA Liberals for nine years, guiding the party to their first state election win in 16 years.
His government was dumped after one term and Peter Malinauskas installed as premier after Labor won 27 seats to the Liberals' 16 in the 47-seat House of Assembly.
In a statement, Mr Marshall said he was proud to lead the Liberal Party and thankful to South Australians for his election as premier in 2018.
"It has been the greatest privilege to serve South Australians over the last nine years and to lead the state as premier through one of the most important and difficult periods in recent history," he said.
"We accomplished incredible things as a Liberal government and, despite the challenges caused by COVID-19, worked tirelessly to ensure South Australia emerges from the pandemic stronger than ever."
Mr Marshall said he looked forward to the future and watching the Liberal Party progress further under the guidance of the new leader.
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