Markit said the pace of increase in August was one of the fastest seen in recent years.
"The flash PMI suggests that the euro zone is still experiencing one of its best periods of economic growth and job creation during the past four years," Rob Dobson, senior economist at Markit, said in a news release.
While Germany performed well, growth in France was pared by further declines in manufacturing production. Job losses were also recorded for a second successive month.
Worse news came from China on Friday, where the final Caixin PMI came in at a two-year low of 47.8 for July. This signaled that business activity in the country is falling.
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—By CNBC's Katy Barnato. Follow her @KatyBarnato.