High court judges have ruled that Dewani must be extradited within 28 days. He is accused of arranging his wife's murder in South Africa but his extradition has been delayed because of his mental health problems.
The Home Office told ITV West Country tonight that he had now exhausted his rights to appeal against extradition. They say the timing of his removal from Britain will be up to the South African authorities and the police.
Honeymoon murder suspect Shrien Dewani has lost his latest legal battle to block extradition to South Africa.
Dewani, 33, from Bristol, has argued that he should not be forced from the UK to face trial over wife Anni's death until he has recovered from mental health problems, including post traumatic stress disorder.
A panel of judges, headed by Lord Chief Justice Lord Thomas, ruled in January that it would not be "unjust and oppressive" to extradite him if an undertaking was given by the South African government relating to how long he would be kept in the country without trial if his illness continues.
The South African authorities have now given the necessary assurances, but Dewani's lawyers returned to London's High Court today to challenge the undertaking.
They also asked for permission to take the case of the millionaire businessman, who is compulsorily detained in hospital under the Mental Health Act, to the Supreme Court, the UK's highest court.
But the judges rejected complaints made about the adequacy of the undertaking and also refused to give the go-ahead for the case to go to the Supreme Court.
Dewani denies any involvement in the killing of 28-year-old Anni, who was shot on the outskirts of Cape Town in November 2010.
Three men have already been convicted over Anni Dewani's death.
South African Xolile Mngeni was convicted of premeditated murder for shooting her. Prosecutors claimed he was a hitman hired by Shrien Dewani to kill his wife, which Dewani has consistently denied.
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 handed a 25-year prison sentence.