The legal team representing Modi said that they were in the process of "challenging" the order in the UK high court.
The UK Home Office has approved the extradition of Indian billionaire jeweler Nirav Modi, a spokesman for the immigration department said on Friday.
"On 25 February the District Judge gave judgment in the extradition case of Nirav Modi. The extradition order was signed on April 15," said the spokesman.
The legal team representing jeweler Modi said that they were in the process of "challenging" the order in the UK high court. India's External Affairs ministry did not immediately respond, according to the Reuters news agency.
Modi had catered to a host of high-profile clients, including Hollywood celebrities, before the fraud came to light
Modi had lost his bid to not be extradited to India in a UK district court in February. At the time, the judge disputed the tycoon's claims that his business was legitimate.
"I find no genuine transactions and believe there is a process of dishonesty. Many of these are a matter for trial in India. I am satisfied again that there is evidence he could be convicted. Prima facie there is a case of money laundering," the judge said.
The court had rejected Modi's argument that he would not be fairly treated in India. Modi had also argued that he had a family history of suicide and depression and his mental health had worsened during the pandemic.
The son of a diamond merchant, Modi built an international empire and opened luxury jewelry stores in several major cities around the world. He also catered to a host of celebrity clients, including actresses Naomi Watts, Kate Winslet and Priyanka Chopra-Jonas. Nirav Modi shares the last name with India's Prime Minister, Narendra Modi, but the two men are not related.
He was arrested in the UK in 2019 at the behest of Indian authorities, who want him to face trial over a $1.8-billion (€1.59-billion) loan fraud at state-run Punjab National Bank (PNB).
Indian authorities allege that companies owned by Modi defrauded PNB — India's second-largest public lender — by using forged documents to raise credit to buy and import jewels.
Modi, one of the main suspects in the case, fled India in early 2018 before the scandal came to light. He denies wrongdoing and says the charges against him are politically motivated.
Another Indian business tycoon, Vijay Mallya, lost an appeal in UK's high court in 2020 against his extradition to India to face fraud charges. He is yet to be extradited to India.