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.
The SA Electoral Commission said the deadline for voters to register would be June 14, while candidate nominations would close on June 17.
Pre-poll voting opens on June 20.
People in isolation or quarantine because of COVID-19 will be able to apply for a postal vote.
Special arrangements will also be put in place for anyone who contracts the virus after the cut-off for postal applications.
At polling booths, officials will be required to be fully vaccinated and wear masks with hygiene officers in place at each location.
At the March election, there were more than 25,000 people registered to vote in Bragg, which includes some of Adelaide's most affluent eastern suburbs.
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