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.
A panel of judges, headed by Lord Chief Justice Lord Thomas, ruled in January that it would not be "unjust" 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 yesterday 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 refused to give the go-ahead.
Dewani is accused of ordering the killing of 28-year-old Anni, who was shot as the couple travelled in a taxi on the outskirts of Cape Town in 2010.
An 11th hour bid to gain more time to continue the fight against extradition was rejected by the court. An application was made to the judges to delay immediately triggering the 28-day period in which the law now requires Dewani to be extradited.
His lawyers said the move was necessary to give the doctors additional time to produce new medical reports that could lead to a reopening of the case.
After the High Court ruling, Anni's father Vinod Hindocha said outside the Royal Courts of Justice: "We are quite happy with the decision and we hope to get the answers that we have been seeking for the past three and a half years."