From the 1950s until 1980, more than 17,000 children were adopted in SA, many through forced removal by agencies or churches.
A Senate report tabled recently recommended all states and territories make official apologies.
Premier Jay Weatherill said that would happen in SA.
"Families need recognition of the fact that in cases when mothers felt pressured to relinquish children they have spent decades dealing with the impact, as have their relinquished children," he said.
"The task ahead of us now is understanding what form that apology should take to ensure that it's sincere for both the birth mothers and fathers, children and extended families.
"In formulating this apology I've asked the Minister for Education and Child Development to engage with community groups and the people most affected by these past practices."
Post-adoption counsellor Evelyn Robinson says the move is welcome.
"We really are setting an example to the rest of the world and I think it's great," she said.
"It's a validation and an acknowledgment for people of what happened, of what their experiences were."
Ms Robinson says the Senate report also mentioned compensation, but she doubts that is a priority for most.
"It's not an issue that is raised very much. I think for most people they're more interested in having their experiences acknowledged and having the truth come out and know that they're being believed," she said.
The apology will be made on June 13.