Shrien and Anni Dewani were on honeymoon in Cape Town in November 2010 when she was killed
Mr Dewani, 34, is accused of ordering the murder of his new wife, 28-year-old Anni, who was shot in Cape Town in November 2010. He denies murder.
The Bristol businessman has been fighting against extradition for three years but lost his latest appeal.
Mr Dewani is expected to appear at Western Cape High Court on Tuesday.
In a statement Scotland Yard said: “Shrien Dewani, 34, has today, 7 April, at approx 20:00hrs been extradited from the UK to South Africa.”
He was taken from Fromeside Hospital, a secure mental health unit in Bristol, to the city’s airport by officers from the Metropolitan Police Service Extradition Unit.
Officers were met at the airport by representatives from the South African authorities who have escorted him on the flight to South Africa.
Mr Dewani was originally arrested by officers from the extradition unit on 7 December 2010 at the request of the South African authorities.
‘What really happened’
The family of Mrs Dewani, a Swedish national, welcomed the extradition adding that they “need justice”.
Mr Dewani and his wife were held at gunpoint while being driven in a taxi through Gugulethu township near Cape Town.
He was thrown from the car later that night and the body of Mrs Dewani was found the next day with a single gunshot wound to the neck.
Anni Dewani’s uncle Ashock Hindocha and brother, Anish Hindocha said they were delighted that Shrien Dewani was to be extradited
Speaking at a news conference earlier, Mrs Dewani’s brother, Anish Hindocha said: “It’s been very difficult.
“There is no life in our family any more, we struggle. With the help of the South African people, with the help of the British people, we are at least trying to cope.”
Mr Hindocha said the protracted legal battle to have Mr Dewani extradited had been “very heavy” for the family.
Mrs Dewani’s uncle, Ashok Hindocha, said the family would be attending the court hearing.
He said: “From today and onwards this case will be about Anni. Until now it hasn’t been about what really happened to her.
“The justice system is the way it is. Obviously we were extremely surprised that it took such a long time. There is one nation, one powerful nation called the United Kingdom, that has a treaty with South Africa.
“That treaty was challenged, so we are happy that it went through. Unfortunately it took a long time.”
Mr Dewani could be held in Valkenberg psychiatric hospital, the BBC understands
Mr Dewani’s lawyers argued that he should not be forced from the UK to face trial until he had recovered from mental health problems, including depression and post-traumatic stress disorder.
But last month judges at the High Court rejected his appeal and denied him the chance to take the case to the Supreme Court.
They agreed with the South African authorities that if Mr Dewani was not fit to stand trial within 18 months he would be returned to the UK.
‘Patient and suspect’
The South African Department of Justice said Mr Dewani will be taken straight to court after he lands and is expected to appear at Western Cape High Court, where he will be formally charged.
He will be accompanied by a doctor, nurse and police officers during the journey, because he is “a patient and suspect who is in police custody”.
Journalists will be allowed to film inside the courtroom but all cameras will have to be switched off as soon as the judge enters the room.
It is understood Mr Dewani’s legal team could apply for bail. If that is refused, he will be taken to the high-care wing of Valkenberg, a psychiatric facility, the BBC’s Karen Schoonbee in Cape Town understands.
Three men have been convicted and jailed over Mrs Dewani’s death, including taxi driver Zola Tongo, who was given 18 years after admitting his role in the killing.
Xolile Mngeni, who prosecutors claim was the hitman, was convicted of premeditated murder over the shooting, and another accomplice, Mziwamadoda Qwabe, pleaded guilty to murder and was handed a 25-year prison sentence.
