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.
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.
Mrs Dewani's uncle Ashok Hindocha described the case as "going through legal torture".
He said: "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."
