The family of Anni Dewani said they have waited "three years, three months" for a ruling that paves the way for her husband Shrien Dewani to be extradited to South Africa to stand trial for her 2010 murder.
Speaking on behalf of family members at London's High Court, Mrs Dewani's first cousin Amit Karia said: "We are happy with the judgment. We have waited for it for three years, three months. .... It seems a step closer to finally getting justice for our Anni."
But he warned there was still a chance that Shrien Dewani could launch a last-ditch appeal over today's ruling to the Supreme Court, the highest court in the land.
Mr Karia said: "We are always worried and don't take anything for granted."
He also described the situation for Anni's parents as "immensely difficult - they do not have normal life any more," adding: "They just want the truth - that is all we have ever wanted."
More top news
The last surviving Dambusters pilot has died at the age of 96.
A British pensioner has reportedly been raped, murdered and set on fire in Bulgaria, just months after she moved to the country.
David Cameron has been urged to visit Calais to witness the impact of the migrant crisis "first-hand".