A judge at Westminster Magistrates' Court decided that it would not be "unjust or oppressive" to extradite the 33-year-old, accused of plotting to kill his Swedish-born Indian wife in South Africa in November 2010.
Dewani's lawyers now have 14 days to appeal against the order. The Bristol-based businessman, who strongly denies any involvement in his wife's murder, was seeking to delay his extradition on account of his mental health.
He had been excused from appearing in court, having been diagnosed with post-traumatic stress disorder and depression and has been receiving treatment at a hospital near his home city.
His risk of suicide is real but not immediate, and while he remains moderately depressed he is better than he was, the court was told.
His lawyers have expressed concerns he would be a high suicide risk if he returned to the country, and his human rights could be breached because of the risk of violent and sexual assaults in jail.
Anni Dewani, 31, was shot when a taxi in which the couple were travelling was hijacked in the Gugulethu township near Cape Town while the couple were on their honeymoon. She was found dead in the back of the abandoned vehicle with a bullet wound to her neck.
Dewani and driver Zola Tongo were ejected from the car before Anni was driven away and killed.
Last year, South African Xolile Mngeni was convicted of premeditated murder for shooting her.
Prosecutors claimed he was a hit-man hired by Shrien Dewani to kill his new wife, something that Dewani has consistently denied.
Tongo was jailed for 18 years after he admitted his part in the crime, and another accomplice, Mziwamadoda Qwabe also pleaded guilty to charges over the murder and was handed a 25-year prison sentence.
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