Mziwamadoda Qwabe pleaded guilty to murder, kidnapping, robbery, murder and illegal possession of a firearm.
Another accused hitman, Xolile Mngeni, has a malignant brain tumour that has so far prevented him from standing trial.
But South Africa is still awaiting the extradition of the victim's husband Shrien Dewani, who is accused of masterminding the November 2010 killing in a murder set up to look like a botched carjacking.
Last week, Britain's High Court temporarily halted Mr Dewani's extradition, citing mental health grounds.
Qwabe's lawyer Daniel Theunissen said a plea agreement had been reached and he had signed it.
"It's a positive step for the prosecution because we are now a step closer to getting information on what happened on that day, which will shed some light on the role played by Shrien Dewani," Eric Ntbazalila, a South African prosecutor said.
Mr Dewani claimed that he was forced out of the car window during the hijacking. According to Mr Ntabazalila, Qwabe's plea bargain contains new information on where he was dropped off by the accused after the alleged hijacking.
Anni Dewani's family reacted by saying they were "happy" but would not know the truth of "what really happened" until Mr Dewani travels to South Africa to face trial. He has previously pledged to fight to clear his name.
Mrs Dewani's uncle Ashok Hindocha said: "We are just happy. Two of the accused have now pleaded guilty. Now we want to know what really happened to Anni, why they killed her."
Mrs Dewani, 28, was shot dead and her body found in an abandoned taxi in Cape Town's impoverished Gugulethu township in November 2010.
Last week, a British court heard that Shrien Dewani needed a year to recover from depression before facing extradition proceedings.
Mr Hindocha said the family were still unable to begin mourning because of the proceedings.
"The way we feel is that we are going through legal torture. It is extremely stressful for the family. I would have been much, much happier if all the accused were in South Africa and cross-examination took place and the truth could be found.
Dewani, 32, is accused of arranging the contract killing of his wife Anni in Cape Town in November 2010, is under medical treatment after being sectioned and deemed a suicide risk.
His barrister, Clare Montgomery QC, said last Tuesday that the process had been hanging over the businessman like "the sword of Damocles" and he needed "a period of calm".
She told Westminster Magistrates' Court in London on 31 July that keeping Dewani under medical treatment in Britain for 12 months would increase the speed of his recovery and warned that sending him to South Africa would jeopardise it.
Dewani's psychiatrist says he is making a slow recovery but one damaging factor is his "constant awareness" of the extradition proceedings, the court heard.
Miss Montgomery said Dewani was taking anti-depressants on the advice of his psychiatrist, who believed his depression and PTSD were of moderate severity and had discernibly decreased.