Its gross domestic product (GDP) was estimated to have expanded 0.6 percent from the last quarter, the fastest rate since the first quarter of 2015 and double the 0.3 percent growth during last year's fourth quarter, according to the bloc's statistical agency Eurostat.
For the first time, the eurozone's economy recovered all its lost ground and returned to levels before the financial crisis in 2008, data showed.
Eurozone's 0.6-percent reading has well beaten a wide expectation of 0.4 percent and outpaced growth rates of the United States and the United Kingdom, which reported 0.5 percent and 0.4 percent growth respectively.
The bloc's gain in the first quarter provided a "solid start" to the year, particularly against a backdrop of recent worries over the global economy, said Jonathan Loynes, chief economist at Capital Economics.
However, economists cautioned that the bloc's growth would slow as two recent sources of support to growth -- the effects of previous declines in the euro and oil prices -- were likely to fade over the coming quarters.
In the wider 28-country European Union, the GDP expanded by 0.5 percent during the first quarter of 2016 compared with the previous quarter and grew by 1.7 percent compared with the same quarter of 2015, Eurostat said.