It follows a three year legal battle by Shrien Dewani against returning to the country where his wife Anni, 28, was shot in November 2010.
Mr Dewani, from Bristol, denies murder and lost his latest appeal against extradition in March.
The couple were held at gunpoint while being driven in a taxi through Gugulethu township near Cape Town.
By Andrew PlantBBC News, Cape Town
Shrien Dewani is expected to land at Cape Town international airport at 06.15 on Tuesday morning and will then be interviewed under caution, before being charged.
He's then expected to be taken to a holding cell before appearing before a judge at Cape Town High Court at about 10:00.
He's expected to spend the night at Valkenberg Hospital, a large psychiatric hospital on the outskirts of Cape Town.
Doctors there will assess whether or not he is mentally fit to stand trial.
South African authorities have 18 months to put him on trial - or return him to the UK.
Cape Town ready for Dewani trial
Timeline: Anni Dewani murder
Mr Dewani was thrown from the car. The body of Mrs Dewani was found the next day in the abandoned taxi with a single gunshot wound to the neck.
Three men have already been convicted in connection with Mrs Dewani's death. Prosecutors in South Africa allege Mr Dewani ordered the killing of his Swedish national wife.
Mr Dewani's legal team still have the option of applying to the European Court of Human Rights, but so far no application has been received.
The businessman, from Bristol, is expected to arrive in Cape Town on Tuesday..
Once on South African soil he is likely to appear before the Western Cape High Court where his 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.
Ashok Hindocha, Anni Dewani's uncle, told ITV's Daybreak that the family would attend the court hearing.
"We want to know what happened to Anni. That is it," he said.
Anish Hindocha, her brother, added: "We are just focusing on this case at the moment and it is hard to even start making the grieving process final yet because there are so many questions we need answers to.
"We hope we get it and now today he is getting extradited and that is one step closer towards what we are seeking for her - that is justice for her."
Mr Dewani is being compulsorily detained in the UK under the Mental Health Act after being diagnosed as suffering from severe depression and post-traumatic stress disorder.
South African Xolile Mngeni was convicted of premeditated murder for shooting Mrs Dewani and jailed for life.
Prosecutors claimed he was hired to carry out the killing.
The couple's taxi driver, Zola Tongo, was jailed for 18 years after he admitted his part in the killing and another accomplice, Mziwamadoda Qwabe, also pleaded guilty to murder and was sentenced to 25 years in prison.
A man accused of arranging his wife's killing on their honeymoon is expected to be extradited to South Africa later.