A Telenor spokesman said Bharti will not pay any cash under the deal but will instead take on the Telenor unit's commitments to pay for licences and phone towers.
The acquisition, which also includes Telenor's India employees and its 44 million customers, will not lead to any impairment charges for Telenor.
The deal highlights how the entry late last year of Reliance Industries' wireless carrier Jio is shaking up India's crowded telecoms sector. With its free voice and deeply discounted data plans, Jio has pushed rivals to slash rates, sharply eroding their profits.
Expectations have grown for continued consolidation, likely culminating in the emergence of a few large players and the exit of smaller players like Telenor, which accumulated losses of 24 billion NOK ($2.87 billion) since entering India in 2008, and has assets in the country of just 0.3 billion NOK.
Britain's Vodafone Group is already in talks to merge its Indian subsidiary with Idea Cellular, potentially overtaking Bharti Airtel as India's largest mobile operator with about $12 billion in sales.
"The decision to exit India has not been taken lightly. After thorough consideration, it is our view that the significant investments needed to secure Telenor India's future business on a standalone basis will not give an acceptable level of return," Sigve Brekke, CEO of Telenor Group, said in a statement.
Shares of Bharti Airtel, in which Singapore Telecommunications is the second-biggest shareholder, rose as much as 11 percent in Mumbai trade to a one-and-a-half year high after the deal was announced. They were up 4.7 percent in early afternoon trade.