The Apax-iGate consortium has offered about 500 rupees a share for the stake, the source said, adding that a deal would likely be announced early next week.
Patni shares closed at 486.40 rupees on the Bombay Stock Exchange on Monday.
The consortium, which beat a rival team of Carlyle, Advent International and Akansa Capital to the deal, will make an open offer for another 20 percent stake in Patni following the agreement, the source said.
Talks to sell a stake in the software services exporter have been going on for about two years, but Patni has failed to seal a deal due to valuation gaps with potential buyers, sources previously told Reuters.
The Patni promoters have to do the deal. They just have to extract that last drop, Arun Kejriwal, strategist, KRIS. And if they (iGate-Apax) are going to raise debt for the acquisition, then it will most likely burden Patni.
The iGate-Apax consortium is taking a loan of about $500 million to fund the deal, the source said.
Patni, iGate and Carlyle were not immediately available for comment.
Patni, a mid-sized IT services firm also listed in New York , provides technology outsourcing services to industries such as insurance, telecoms, utilities and retail.
Small and mid-cap Indian IT companies have been grappling with tepid demand, high attrition rates and a rise in expenses, resulting in reduced profitability for some.
The founding Patni brothers are selling their 46 percent stake, while private equity firm General Atlantic is selling its roughly 17 percent holding in the software services exporter, sources have previously told Reuters.
Private equity activity is surging in India, with $6.57 billion invested in the first three quarters of 2010, more than double the $2.5 billion invested during the same period last year, according to Venture Intelligence, a research firm.
Private equity firms typically make minority investments in India, where entrepreneurs are often reluctant to sell out and where full buyouts are rare.
Local media had earlier reported that private equity firms including Apax and Providence Equity had shown interest in buying BT Group's stake in Tech Mahindra that is likely to be valued at $830 million.
(Additional reporting by Bharghavi Nagaraju; Editing by Jui Chakravorty and Jon Loades-carter)