Cap Gemini, the market capitalisation of which was about 13 billion euros ($14 billion) at the close of business on Friday, said it would pay $48 a share for IGATE. The U.S. company's shares on NASDAQ stood at $45.85 at Friday's close.
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The deal will be financed through a combination of Cap Gemini's own cash, debt and an equity portion that will not exceed a 6 percent dilution of the French company's share capital.
Cap Gemini said it had the backing of shareholders representing 54 percent of IGATE's share capital and that the deal would enhance earnings by 12 percent in 2016 and 16 percent in 2017.
After completion, North America will represent 30 percent of estimated combined 2015 revenue of 12.5 billion euros ($13.58 billion), raising Cap Gemini's revenue in the region by about a third. The combined group's operating margin will be above 10 percent, it said
IGATE has about 80 percent of its operations in North America, which Cap Gemini said is "by far the largest and most innovative technology and services market in the world".
The acquisition will strengthen its businesses in application and infrastructure services as well as business process outsourcing and engineering services, also adding new flagship clients such as General Electric and Royal Bank of Canada.
In a separate statement bringing forward its first-quarter revenue announcement, Cap Gemini said that sales grew by 10.5 percent in the quarter and reset its revenue growth target to "at least 5 percent" from its previous forecast of between 3 percent and 5 percent.