Modi, 48, owned luxury jewellery stores in several major cities across the world and boasted celebrity customers including actresses Naomi Watts, Kate Winslet and Priyanka Chopra-Jonas before his downfall last year.
A spokesman for London's Metropolitan Police told AFP that Modi was arrested on behalf of the Indian authorities in the British capital on Tuesday.
He was due to appear at a London court on Wednesday, the spokesman said.
Modi fled India in February 2018 after being accusd of having a central role in a $1.8-billion fraud involving Punjab National Bank (PNB), the country's second-largest public lender.
Earlier this month, Indian authorities dynamited the fugitive billionaire's multi-million-dollar seafront mansion.
The 33,000 square-foot (3,000 square metre) property near Mumbai, believed to be worth $14 million, had been seized.
Forbes estimated Modi's wealth at $1.73 billion before the alleged fraud, placing him 85th on India's rich list.