Nehru, 69, a cousin of Rajiv Gandhi and Minister for Internal Security in his government, had been admitted to the Fortis hospital in Gurgaon 18 days ago and passed away at 10.47 pm, family sources said.
He is survived by his wife Subhadra and two daughters.
Lucknow-born Nehru was a three-time Lok Sabha member.
Nehru had a successful career in the corporate world before joining politics in the early 1980s.
When Rajiv Gandhi became the Prime Minister in 1984, he was his close adviser and Minister of State for Internal Security. However, he fell out with Rajiv later.
Nehru was accused by the CBI of causing a loss to the exchequer in a pistol deal with Czechoslovakia in 1988 during his tenure as Minister of State.
The Supreme Court had recently stayed the proceedings in the case.
Nehru moved out of the family home in Allahabad at an early age and studied at the La Martinere Boys College in Lucknow. At the age of 20, he began a successful career in the corporate world, which he gave up 17 years later when Indira Gandhi asked him to join politics. Nehru was then the president of the Jenson and Nicholson group of companies.
Lord Swraj Paul, who had known Nehru closely for several decades, mourned his death and said he was a very warm person and a loyal friend.
"He was a wonderful human being. My heart goes to the family in this hour of gried," he said.
Janata Dal-United leader Sharad Yadav described Arun Nehru as a "leader with political maturity" who played a key role in formation of the Janata Dal government.
Nehru's funeral will take place at the Lodhi crematorium in New Delhi on Friday
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