"Lawyers acting for Shrien Dewani will review today's [Wednesday] judgment and lodge an appeal during which time Shrien will remain in the UK," Dewani's family said in a statement after the ruling on Wednesday.
"Shrien Dewani remains unfit to be extradited or to face trial. Shrien remains committed to returning to South Africa when his health would permit a full trial and when appropriate protections are in place for his health and safety.
"The legal process is ongoing and it would be inappropriate to comment further," the statement reportedly read.
Chief Magistrate Howard Riddle made his ruling in the Westminster Magistrate's Court despite arguments by Dewani's defence team that he could suffer setbacks in his mental health if sent back now.
They wanted the decision delayed by six months. The 33-year-old British businessman had earlier been diagnosed with depression and post-traumatic stress disorder.
The courtroom was packed with murdered Anni Dewani's relatives, who wore photographs of her pinned to their clothes, decorated with pink ribbons.
'Dewani will recover'
Riddle said: "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.
"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.
"It is not impossible that if returned now, then after a reasonable period of further treatment and assessment he will be found fit to plead and a trial can take place."
Dewani has undergone treatment for post-traumatic stress disorder and depression since his wife's death.
Dewani is suspected of ordering the killing of his new wife Anni (28), who was shot as the couple travelled in a taxi on the outskirts of Cape Town in November 2010.
So far three men have been convicted over Anni's death.
Hitman hired by Dewani
Last year, Xolile Mngeni was convicted of premeditated murder for shooting her and was sentenced to life imprisonment.
Prosecutors claimed he was a hitman hired by Dewani to kill his wife, something that 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.
Riddle ruled in 2011 that Dewani should be extradited, but this was successfully appealed against and he was ordered to look again at the case. – Sapa