The Hackett research finds also that of 5.1 million business services jobs remaining in the U.S. and Europe in 2012 -- including slightly more than two million in finance jobs -- about 1.8 million have the potential to be moved offshore, with 750,000 of those moving by 2016. In those totals, nearly 705,000 of the 1.8 million, and 328,000 of the 750,000 are in finance.

"So by the end of the next 8-10 years, the traditional model of lifting and shifting work out of Western economies into low cost geographies will cease to be major factor driving business services job losses in the U.S. and European," according to Hackett.

Michel Janssen, Hackett's chief research officer, says that the trend "is going to continue to hit us hard in the short-term. But after the offshoring spike driven by the Great Recession in 2009, the well is clearly beginning to dry up. A decade from now the landscape will have fundamentally changed, and the flow of business services jobs to India and other low-cost countries will have ceased."

He adds that related cost-control challenges will be great for U.S. and European companies, which now on increased offshoring to help drive down costs in IT, finance, and other business services areas. "But other opportunities for improving efficiency still exist, particularly automation, and end-to-end process improvements to streamline how business services are provided."