Tycoon Mukesh Ambani launched Reliance Jio's 4G network in September with an audacious free service for the rest of 2016, followed by vastly cheaper data plans and free voice calls for life.
The move forced rivals to slash their tariffs and scramble to match the deep pockets of Jio, which is backed by Ambani's vast energy-to-chemicals conglomerate Reliance Industries and picked up 100 million subscribers in its first six months
Bharti's acquisition is the latest movement towards consolidation in India's telecoms sector as major players try to position themselves to best face the tough new environment.
The move, which still needs to be approved by regulators, will enhance its coverage, the company said in a statement to the Bombay Stock Exchange (BSE), and see Telenor exit India.
"The proposed acquisition will include transfer of all of Telenor India's assets and customers, further augmenting Airtel's overall base and network," the Indian firm said in the statement.
Last month British mobile phone behemoth Vodafone announced that it was in talks to merge its Indian unit with Mumbai-based Idea Cellular in its own move to counter Jio's rise.
That deal would create India's largest telecoms company. Global brokerage firm CLSA estimated that the pair would command a combined 43 percent share of market revenue, ahead of Airtel, which is currently the market leader, on 33 percent.
Reliance Communications -- owned by Ambani's brother Anil Ambani -- and Tata Teleservices, part of the sprawling salt-to-steel Tata conglomerate, are also reportedly in talks to join forces.
Reliance merged with telecom operator Aircel in September last year. Bharti Airtel's shares surged more than five percent in Mumbai morning trade following the Telenor deal announcement.
"The decision to exit India has not been taken lightly," Sigve Brekke, Telenor Group CEO, said in the statement.
"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," he added.
Telecoms analyst Baburajan Kizhakedath said Telenor was quitting India because the intense competition meant there was no scope for growth. "The Airtel-Telenor deal is probably the best exit route for Telenor," he told AFP.