The Dewani family welcomed the ruling, saying: "Shrien can only return to South Africa when he is well enough and when his personal safety can be guaranteed."
Sir John Thomas, president of the Queen's Bench Division and Mr Justice Ouseley, allowed Dewani's appeal against immediate extradition and ordered that the case be remitted back to Westminster Magistrates Court for a further hearing.
The key factors the judges said they had taken into account included his unfitness to plead, increased prospects of a speedier recovery if he remains in the UK and "the lack of clear certainty" as to what would happen if he was returned to South Africa in his present condition.
The risk of suicide was also considered "to a much lesser degree".
Mrs Dewani, 28, from Sweden, was shot when a taxi the couple were travelling in was hijacked in the Gugulethu township on the outskirts of Cape Town.
She was found dead in the back of the abandoned vehicle with a bullet wound to her neck after taxi driver Zola Tongo drove the newlyweds to the impoverished area.
He and Mr Dewani were ejected by the hijackers before Mrs Dewani was driven away and shot.
Tongo, who has admitted his part in the crime, claimed in a plea agreement with prosecutors that Dewani ordered the carjacking and paid for a hit on his wife.
Home Secretary Theresa May signed an order for his extradition after District Judge Howard Riddle ruled at Belmarsh Magistrates' Court in south east London last August that Dewani should be sent back to South Africa to stand trial.
But at a High Court hearing in December two judges heard that the health, and the life, of the businessman - who has been diagnosed with severe post-traumatic stress disorder (PTSD) and severe depression - will be at risk if he is extradited.
Sir John Thomas, president of the Queen's Bench Division, and Mr Justice Ouseley, were urged to block the extradition order on the grounds that his mental health had deteriorated to the point where he was ''too ill to be extradited'' and was a suicide risk.
At the December hearing Clare Montgomery QC, for Dewani, also argued he was at serious risk of violence if kept in custody in South Africa, including sexual violence, at the hands of other prisoners.
Mrs Dewani, 28, from Sweden, was shot when a taxi the couple were travelling in was hijacked in the Gugulethu township on the outskirts of Cape Town.
She was found dead in the back of the abandoned vehicle with a bullet wound to her neck after taxi driver Zola Tongo drove the newlyweds to the impoverished area.
He and Mr Dewani were ejected by the hijackers before Mrs Dewani was driven away and shot.
Tongo, who has admitted his part in the crime, claimed in a plea agreement with prosecutors that Dewani ordered the carjacking and paid for a hit on his wife.
Ms Montgomery argued he was so ill that he would be incapable of giving instructions to his lawyers or following trial proceedings, and extradition should be delayed until he had recovered.
The QC told the judges that Dewani had always wished for a fair trial.
''However that is, at the moment, on the advice we have been given by those who are treating him, not possible,'' he said.
His illnesses had begun to develop shortly after the murder of his wife and before he was accused of her murder.
All the doctors who had examined him, including the expert instructed by the South African government, agreed that he was suffering from PTSD and depression, said Ms Montgomery.
She asked the judges to discharge the extradition order, or adjourn its implementation.
The QC submitted that District Judge Riddle had fallen into error when he accepted South African assurances that Dewani's life and health would not be endangered if he was sent back to South Africa.
She argued the limited assurances that were given were ''incapable of fulfilment''.
Ms Montgomery told the court Judge Riddle should have ordered Dewani's discharge under section 91 of the Extradition Act 2003 on the grounds that sending him back would ''manifestly endanger his health or risk his life''.
The move was opposed by the South African government.
In a statement released last night, the Dewani family said the allegations against him were ''deeply flawed'' and he was determined to return to South Africa to clear his name and seek justice for his wife.
The correct place to demonstrate his innocence was in a court of law, the statement said, adding: ''This can only be done when he is well enough and when his personal safety can be guaranteed.
''The family remain hopeful that the British High Court will block any attempt to extradite Shrien until he has fully recovered and it is safe for him to stand trial, if charged.''
The Dewani family's lawyer, Charlotte Harris, of Mishcon de Reya, said in a statement: ''Shrien is innocent and has always maintained his commitment to clearing his name of all the false allegations and slurs against him. He remains determined to fight for justice for his wife, Anni.''
