Compared with the fourth quarter of 2012, the rate of expansion was even higher at 0.5 percent, Eurostat said.
EU expects continued recovery
The latest figures are good news for the 18-nation currency area which suffered the longest recession in its decade-long history following the sovereign debt crisis in 2009.
According to the Eurostat figures, the recovery was led by the bloc's main economies, Germany and France, which expanded by 0.4 percent and 0.3 percent respectively.
But the biggest quarterly rises were posted by new eurozone member Latvia, up 0.7 percent, and the Netherlands which grew by the same rate. Italy, which is the euro area's third-biggest economy, grew by only 0.1 percent.
Eurozone laggard Greece saw its economic problems ease somewhat at the end of 2013, logging a better-than expected contraction of 2.6 percent on the annual comparison for the quarter.
Eurostat data also showed even better fourth-quarter growth for the wider 28-nation European Union. There, gross domestic product (GDP) grew 0.4 percent, up from 0.3 percent in the third quarter.
Non-euro Britain expanded 0.7 percent as it continued to lead among the bloc's top economies.
The largest gains were seen in the emerging regions of Eastern Europe, where Poland and Hungary increased their quarterly output by 0.6 percent each, and Romania jumped 1.7 percent.