A judge at Westminster Magistrates' Court here 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.
Anni, 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.
A spokesperson for his family said the defence team would review the judgment and lodge an appeal, during which time Dewani would remain in the UK.
"Shrien Dewani remains unfit to be extradited or to face trial," said the spokesperson.
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 (PTSD) and depression and has been receiving treatment at a hospital near his home city.
"It is not in question that Shrien Dewani will be returned to South Africa. The treating clinicians continue to state that Mr Dewani will recover," said District Judge Howard Riddle in his ruling.
"There has been recovery, but it has been slow. It may be a long time before Mr Dewani is fit to plead, but he may be closer to that point," he added.
Judge Riddle had ruled back in 2011 that Dewani should be sent back to South Africa to stand trial but this was successfully appealed against and he was ordered to look again at the case.
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