The combined entity would have almost 400 million customers, overtaking market leader Bharti Airtel to account for about 40 percent of revenue of the world's second-biggest mobile phone services market by users after China.
The deal underscores how India's mobile industry is being transformed by the launch last year of Reliance Jio Infocomm's 4G mobile broadband network.
Built at a cost of more than $20 billion by India's richest man, Mukesh Ambani, Jio has offered free services for months. That has forced India's three biggest operators - Bharti, Vodafone and Idea - to slash prices and accept lower profits, and sparked a wave of consolidation in the sector.
"We are very complementary," Vodafone Chief Executive Vittorio Colao told a news conference in Mumbai after the deal was announced.
"Idea is strong where Vodafone is weaker, Vodafone is strong where Idea is weaker."
The two companies, which announced in January that they were in talks, will have to shed spectrum in some areas to meet India's rules, although Colao said it would be "small". The deal is expected to close in 2018.
Shares in Idea rose as much as 14.3 percent immediately after the news but then fell 9 percent as traders said the implied deal price for Idea was well below the stock's close on Friday. Vodafone shares were flat in London trading as of 0942 GMT.
Idea said the rough deal price worked out to 72.5 rupees per share but stressed that was only for illustrative purposes and was not the actual price. Idea's shares closed at 108.10 rupees on Friday.
Vodafone, the world's second-largest cellphone operator, will own 45.1 percent of the merged entity, after it transfers about 4.9 percent to promoters of Idea or their affiliates for 38.74 billion rupees ($592.15 million) in cash, Idea said.
Aditya Birla Group, the majority owner of Idea, will own 26 percent while other shareholders will own the remaining 28.9 percent. Aditya Birla and Vodafone eventually aim to own an equal share of the joint venture, with a combined enterprise value of $23.2 billion.
Idea would have the sole right to appoint the chairman, while Vodafone would appoint the chief financial officer. The appointment of a chief executive officer and a chief operating officer would require the approval of both companies, which would get the right to nominate three board members each.
Vodafone, which will cut its net debt by about $8.2 billion with the deal, has endured a tumultuous ride since it entered India in 2007, with a high-profile tax battle and a long-delayed Indian listing. The South Asian country contributes more than 10 percent of its revenues.
Colao said on Friday the pending case, with India demanding more than $2 billion in taxes, will not affect the deal, which needs regulatory approval.
The deal does not include Vodafone's 42 percent stake in Indus Towers, a joint venture between the British group, a unit of Bharti Airtel and Idea. But Vodafone and Idea said they will look to reduce their tower assets exposure, including selling their stakes in the joint venture.
Analysts have said Jio's entry is the catalyst for mergers and exits of some foreign players.
Bharti Airtel is in the process of buying Telenor's India operations, while two smaller players controlled by Malaysia's Maxis and Russia's Sistema are merging their operations with Reliance Communications' wireless unit.
"Consolidation is a much anticipated and very welcome development in this beleaguered telecom sector," said Arpita Pal Agrawal, a partner and telecom analyst at PwC India.