Prosecutors in Cape Town announced yesterday that Mziwamadoda Qwabe admitted his part in the murder plus kidnapping, robbery and the illegal possession of a firearm.
The family of Anni Dewani's said they were happy but would not know the truth of what really happened until Mr Dewani, the victim's husband, travels to South Africa to face trial.
Mr Dewani, a former chartered accountant from Bristol, remains in medical care following a breakdown and will not be extradited until his condition has improved.
He has pledged to fight to clear his name.
The body of Swedish national Mrs Dewani, 28, was found in an abandoned taxi in Cape Town's impoverished Gugulethu township in November 2010 after she was shot dead.
The body was discovered soon after the couple's three-day wedding in Mumbai.
The other accused, Xolile Mngeni, still faces charges over the killing and the victim's husband remains in medical care pending a decision on extraditing him to South Africa.
Mrs Dewani's uncle Ashok Hindocha said: "We are just happy. Now we want to know what really happened to Anni."
Mr Hindocha said the family was still unable to begin mourning because of the proceedings.
He said: "With a case like this, everything comes back again.
"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.
"To us, Anni is still not dead.
"We haven't started the mourning process, we can't. We need to know what happened and then we can start working our way through it.
"We know Anni is not coming back.
"Yes, there are people sitting in custody and various reasons have been given for not going forward, but it is not human."
It was not clear what plea deal was agreed with prosecutors in South Africa.
The trial has been postponed several times due to the poor health of Mr Mngeni, who has been diagnosed with a brain tumour.
In March, a High Court in Britain ruled it would be "unjust and oppressive" to extradite Shrien Dewani to South Africa.
The judges said his mental condition had worsened since his arrest in December 2010, and he should not be extradited in his current state.
However, they said it was likely he would recover "within a reasonable time" and could then be sent to South Africa.
Mr Dewani, who has been treated in a psychiatric hospital, claims the couple's vehicle was attacked by gunmen during a township tour.
He was allowed to leave South Africa before a confession by taxi driver Zola Tongo in 2010.
Mr Tongo said he offered him 15,000 rand, about £1200, to arrange the killing and make it look like a carjacking.
In a plea bargain to avoid a life sentence, Tongo pled guilty and was convicted of kidnapping, murder, aggravated robbery and obstructing justice. He was sentenced to 18 years in prison, and is expected to give evidence.
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