The jobless rate in the countries that share the euro as currency rose for the fourth consecutive month, hitting the highest level since the eurozone was created in January 1999.
For the 27-member European Union, the unemployment rate climbed from 10.2 percent in April to 10.3 percent in May, the statistics agency said.
A year earlier, the unemployment rates were 10 percent in the eurozone and 9.5 percent in the European Union.
Eurostat said 24.86 million men and women in the EU were without work, 17.56 million of whom live in the eurozone.
Compared with April, the number of unemployed rose by 151,000 in the European Union and 88,000 in the eurozone.
The unemployment rate rose from 4 percent to 4.1 percent in Austria, but it remains the country in the European Union with the lowest rate, followed by the Netherlands with unemployment rising from 5 percent to 5.1 percent and Luxembourg with unemployment rising to 5.4 percent.
The highest unemployment rate in the EU is in Spain with a rate of 24.6 percent. In Greece, the rate rose to 21.9 percent.