Shrien Dewani, 33, from Bristol, is expected to leave London and arrive in Cape Town on 8 April.
He has been fighting a return to South Africa to face the charges, which he denies, over the death of his wife Anni, 28, in November 2010.
The extradition date was confirmed by South Africa's Department for Justice, the BBC reported.
Dewani had lost his final appeal against extradition at the start of March which triggered a 28-day period during which he must be extradited.
His legal team had wanted the appeal to be heard in the highest court in the land - the Supreme Court - but this was refused by a panel of judges.
The businessman is being compulsorily detained under the Mental Health Act after being diagnosed as suffering from severe depression and post-traumatic stress disorder.
In January, the High Court ruled it would not be "unjust and oppressive" to extradite Dewani providing that assurances were received from South Africa about the length of time he would be kept in the country without trial.
Prosecutors in South Africa allege Dewani ordered the killing of his wife, who was a Swedish national.
The charge dates back to November 2010 when the pair were held at gunpoint while driving through Gugulethu, a township near Cape Town, in a taxi.
Dewani escaped unharmed but his wife's body was found the following day.
Three men have been convicted over Dewani's death.
South African Xolile Mngeni was convicted of premeditated murder for shooting her 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.
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