Publicis, whose attempts to merge with US group Omnicom and create the world's biggest advertising company failed earlier this year, said it had agreed to pay $25 a share for Boston-based Sapient.
The French group said that in acquiring Sapient, its digital operations now represented more than half its business "three years before the goal set out in our strategic plan".
Markets seemed unimpressed with the deal, however, with Publicis shares dropping 3.3 percent while the wider French stock market was broadly flat.
The failure of the Omnicom deal, which would have created an advertising giant to overtake Britain's WPP employing 130,000 staff with annual sales of EUR 20 billion, led to a boardroom shake-up at Publicis.
Chief executive Maurice Levy, 72, decided to stay on until 2017 as the head of the firm in the wake of the collapsed deal, despite previously pledging to leave when his term expires next year.
Meanwhile, chief operating officer Jean-Yves Naouri, once tipped to succeed Levy, left as part of a major reshuffle of the senior executive team.
Publicis said at the time that the deal fell through because of deep differences that widened during the negotiations, administrative problems, and an unduly long timetable.
Sapient, a pioneer of Internet-based technology, had turnover of $1.36 billion (roughly Rs. 8,300 crores) and profits of $85.9 million (roughly Rs. 527 crores) in its last financial year.
On Friday, speculation about the imminent Publicis deal pushed Sapient's shares up 2.79 percent to $17.32 on the US tech-heavy Nasdaq exchange.
Levy warned in July it would be a "difficult year" for Publicis, as the group reported that net profit for the first half of the year fell by 16.9 percent to EUR 260 million, weighed down by the strength of the euro.
Sales were about steady compared with the equivalent figure last year, showing a gain of 0.2 percent to EUR 3.365 billion, but performance slowed sharply in the second quarter.
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