The bloc’s GDP grew by 0.3% in the second quarter of 2013, slightly ahead of forecasts, the Eurostat agency said.
The growth was widely expected after the German economy rose 0.7% between April and June.
However, the overall figure masks the mixed economic fortunes among the countries that make up the 17-country eurozone area.
Germany and France both posted stronger-than-expected growth, expanding 0.7% and 0.5% respectively.
Portugal, among the smallest and the weakest eurozone economies, showed the fastest growth, at 1.1%.
The country was one of three that had to take a multi-billion-euro bailout.
But Spain, which had to seek outside support for its struggling banking sector, saw its economic output fall by 0.1% on the quarter.
Italy and the Netherlands both saw output drop by 0.2%.
European Commission Vice-President Olli Rehn said the figures suggested the European economy was gradually gaining momentum, but added there was no room for complacency.
“There are still substantial obstacles to overcome: the growth figures remain low and the tentative signs of growth are still fragile,” he said.
“A number of member states still have unacceptably high unemployment rates; the implementation of essential, but difficult reforms across the EU is still in its early stages. So there is still a very long way to go.”
Analysts from Capital Economics said: “The return to modest rates of economic growth in the eurozone as a whole won’t address the deep-seated economic and fiscal problems of the peripheral countries.”
The figures reaffirm Germany’s position as the powerhouse behind the eurozone.
The country narrowly avoided recession earlier this year, but GDP in the second quarter of 2013 was driven up by demand from both consumers and businesses.
The improvement comes just weeks before a federal election that will see Chancellor Angela Merkel stand for a third term in office.
Her economic adviser, Michael Fuchs, said Germany had a great chance to be a “locomotive” that led European growth.
But he was also upbeat about the prospects of struggling eurozone members.
“I do believe that some of the countries in the periphery, I mean southern periphery, are doing better than expected,” he said.
“I mean, if you see Spain… in Spain, the last three quarters, the unemployment rate went down. It’s getting slightly better.
“They did reforms, maybe not enough yet, but I believe that at the end of the day they will be competitive again, but it takes some time.”
Do you live in the eurozone? What are economic conditions like at the moment? Send us your comments and experiences using the form below.