Charlie Stevens, 18, sustained an irreversible brain injury after being run down about 9pm on Friday in Goolwa, about 90km southeast of Adelaide, an emotional SA Police Deputy Commissioner Linda Williams told reporters.
Police said the 18-year-old driver failed to stop at the scene but was found nearby.
He has been charged with causing harm by dangerous driving, aggravated driving without due care, leaving the scene of a serious crash and failing to truthfully answer questions.
The man has been refused bail and will face Christies Beach Magistrates Court on Monday.
Premier Peter Malinauskas said the thoughts of all South Australians were with the commissioner.
Police said Charlie died surrounded by family and friends about 7pm on Saturday.
In a statement, Commissioner Grant Stevens and his wife Emma thanked police, first responders and other emergency services workers who attended the incident.
"The Stevens family also wish to thank the wider community for their support during this difficult time in particular the family acknowledge the dedicated staff at the Flinders Medical Centre for their care and support of Charlie and his family and friends," they said.
Premier Peter Malinauskas said the thoughts of all South Australians were with Mr and Mrs Stevens and their children.
"Grant Stevens has served South Australia as a member of South Australian Police for over 40 years," Mr Malinauskas said.
"His whole life he has dedicated himself to protecting others, protecting South Australians from evil, protecting us from disease.
"He has shown extraordinary leadership in some of the most difficult circumstances this state has ever confronted, and it is just so unjust that he and his family have now had to endure this great tragedy themselves."
Ms Williams said Charlie was an apprentice carpenter who had recently finished school.
It was unclear what brought the 18-year-old alleged offender to Goolwa, but Charlie was there celebrating schoolies with his friends.
"He is with his family who are waiting for other family members from interstate to arrive," the deputy commissioner said.
"As you can imagine, this is a very difficult statement for me to make.
Just hours after Police Commissioner Grant Stevens spent the day supporting and grieving with the family and colleagues of Brevet Sergeant Jason Doig, he received the tragic news that his son Charlie was struck by a car in Goolwa.— Peter Malinauskas (@PMalinauskasMP) November 18, 2023
"We always talk about this happening to other people but the reality is it can happen to anyone."
The driver's mother released a statement on Saturday afternoon.
"I extend my deepest possible sympathies to the Stevens family and my heart is breaking to think of the suffering and pain they are experiencing," she said.
"Out of respect and acknowledging that this is now a matter for the courts, I won't be saying anything further at this time."
The alleged hit-run was the second incident to plunge the South Australian policing family into mourning on Friday.
Mr Malinauskas said he was discussing the fatal shooting of Brevet Sergeant Jason Doig at Senior, in SA's southeast, with Mr Stevens just hours before the commissioner learned of his son's involvement in the Goolwa collision.
The premier said it struck him just how determined Mr Stevens was in ensuring the welfare of his colleagues following the deadly shootout.
Major crime detectives continue to investigate the Goolwa incident.
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