Parliamentary Speaker Dan Cregan has confirmed the poll will be held on July 2.
It was forced by Ms Chapman's decision to quit parliament just weeks after being returned at the March state election.
In a brief statement in the House of Assembly on Wednesday, Mr Cregan said he had contacted the electoral commissioner about the suitable date.
"I will today issue the writs to effect a by-election in the electoral district of Bragg on Saturday, July 2," he said.
The SA Greens have already confirmed community campaigner Jim Bastiras will be the party's candidate, while the Labor government and the Liberal opposition are yet to confirm theirs.
Rick Sarre, who ran for Labor in March, has indicated he is willing to run again, while two women and two men are vying for the Liberal pre-selection.
The success of independent candidates in the recent federal election could also prompt a number to nominate, though none have indicated their intentions so far.
Ms Chapman held Bragg with a margin of 16.6 per cent at the 2018 state election but that was cut to 8.2 per cent in March.
If the Liberals hold the seat, the opposition will have 16 seats in the 47-seat House of Assembly.
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