"But there are conditions," the official, who asked not to be named, said.
He said he could not immediately disclose the riders attached to the FIPB's approval of the 9 million deal.
The agreement is now expected to go to the Cabinet Committee on Economic Affairs chaired by Prime Minister Manmohan Singh, and the deal could still need other approvals.
The deal is regarded as a key test of India's ability to attract outside investors to its ailing airline sector, after it began easing foreign investment curbs in sectors from aviation to retail last September.
Jet Airways and Etihad Airways officials were not immediately available for comment.
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Jet said in April it planned to sell a 24 percent stake to Etihad, but the deal stirred wide political controversy in India amid questions about which country would control the Indian airline.