"The improvement was broad-based by sector. Growth of services business activity and new business both hit the highest since May 2011, accompanied by stronger rates of increase in both manufacturing output and new orders to the highest since May of last year," Markit said in a release.
In the euro zone's largest economy, Germany, business activity growth accelerated to the highest point in eight months. It's composite PMI came in at 55.3 in March, up from February's 53.8, with new order growth hitting a nine-month record.
In France, meanwhile, business activity expanded for the second successive month -- coming in at 51.7 in March -- although the rate of growth slowed from February's 42-month high of 52.2.
Chris Williamson, chief economist at Markit, said the data was "welcome news" for the region, which is awaiting signs that the European Central Bank's (ECB) new quantitative easing program is stimulating the real economy.
Given the data, Williamson said he expects gross domestic product (GDP) to have expanded by 0.3 percent in the first quarter of the year.
The data comes after consumer confidence jumped to a near-eight-year high in March, flash data released by the European Commission on Monday showed -- the sharpest monthly gain in confidence since April 2009.
Howard Archer, chief U.K. and European economist at IHS, said that both data show that "euro zone economic activity is strengthening as very low oil prices, a weak euro, major ECB stimulus and much reduced fiscal headwinds foster an improved growth environment."