The deal is part of Vodafone's plan first announced last October to take full control of the unit for a total Rs 101.41 billion, following a change in rules allowing foreign companies to own up to 100 per cent of Indian telecommunication carriers.
Vodafone, which entered India in 2007 by buying Hutchison Whampoa's local cellular assets in a $11 billion deal, directly and indirectly owns a combined 84.5 per cent of Vodafone India, the country's one of the top telecoms company by users and revenue.
Vodafone received the Indian cabinet's approval in February to buy stakes from its minority Indian partners -- Piramal and Indian businessman Analjit Singh.
Piramal had bought the 11 per cent stake in Vodafone India in two tranches during the financial year to March 2012 for Rs 58.64 billion. It is selling the stake to Prime Metals Ltd, which it said is an indirect subsidiary of Vodafone Group.
Piramal shares rose as much as 7.1 per cent after the announcement.
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