A magistrate ruled that Carl Pistorius, 28, had not been negligent in the death of Marietjie Barnard in March 2008.
The prosecution admitted it had been unable to prove the charges and said it would take no further action.
The case had attracted attention as it came to court shortly after Oscar Pistorius shot dead his girlfriend.
He is charged with premeditated murder for the Valentine’s Day shooting, but says he mistook Reeva Steenkamp for a burglar.
Carl Pistorius cried with relief, reported AP news agency, as the magistrate acquitted him of the charges against him, which also included reckless driving.
Instead, the magistrate ruled, Mrs Barnard, 36, had been driving excessively fast when she crashed into the back of his vehicle.
“We are satisfied with the outcome and Carl is also happy to see the end of this case,” said his lawyer Kenny Oldwage following the hearing at Vanderbijlpark Magistrate’s Court south of Johannesburg.
Carl Pistorius said he felt for the family of the woman who had died, AP reported.
“My heart goes to them. I do think of them, and I will continue thinking of them while I walk on this Earth, and I understand their loss and their pain and, regardless of whose responsibility it is, the pain doesn’t diminish.”