The eurozone composite PMI rose to 51.5 (flash 51.7) in August from 50.5 in July, indicating the fastest rate of growth since 2011.
The services index increased to 50.7 (51) from 49.8, representing the first increase in activity for a year and a half.
"The eurozone recovery is looking increasingly broad-based, with more sectors and more countries emerging from recession," says Markit.
"Domestic demand is starting to pick up...with the region’s retail PMI also moving into positive territory for the first time in over two years."
Spain and Italy have joined Germany in returning to growth, while France's decline is far weaker than earlier in the year.
However, job losses continue.
EU Stoxx 50 -0.8%, euro flat vs dollar after being higher earlier. (PR)