Eleanor Payne and Samantha Lake, both 19, were killed when their driver apparently lost control on a bend on Thursday.
Student Daniel Greenwood, 22, died later in hospital following emergency treatment.
The trio were among a group of 18 students and two teachers from Brooksby Melton College, in Leicestershire, and were studying for a foundation degree in animal management and welfare.
They were on a wildlife study tour in the region and were travelling from Swaziland to Nelspruit to visit a monkey sanctuary when their bus overturned a few miles from Barberton.
Students ranging in age from 18 to 30 are understood to have suffered injuries that include a fractured spine, head and facial lacerations, and broken ribs and collar bones.
Friends and relatives yesterday expressed their shock as they tried to come to terms with the news.
Meanwhile, six survivors discharged from hospital were said to be traumatised and upset.
Speaking from her family home – a farm in Hinckley in Leicestershire – Miss Payne's sister Lauren was overcome with emotion.
"We need to have time to grieve for Eleanor," she said.
Miss Payne had worked part-time at a cattery owned by family friend Diane Smith, 57, to raise money for the trip.
She had been looking forward to the adventure for some time and had expressed her excitement on Facebook.
The proprietor of Holly Lodge Boarding Cattery, in Nuneaton, described Miss Payne as "a wonderful girl" with a "lovely personality".
"I'm still in shock at the moment," the proprietor said.
"She was here every Sunday working for us, saving money for South Africa. "
Mr Greenwood was "a nice enough lad to say hello to", neighbour Alan Jordan, 69, said. "His mum and dad lived abroad in Spain and he lived with his grandma."
Friends left online tributes to Miss Lake, known as Sami.
"RIP Sami Lake," one said. "Will never forget you and all the laughs we had up town."