The agency stated that the consumer price index in the euro area rose last month by 8.6% annually, compared to 8.1% in May.
The preliminary estimates issued earlier this month were the same as the final estimates issued today.
At the same time, the core inflation rate, which excludes the most volatile food and energy prices, declined to 3.7% last month, compared to 3.8% according to preliminary estimates.
The record level of inflation was driven by an annual increase in energy prices of 42%, an increase in food prices by 8.9%, and prices of industrial goods other than energy by 4.3%, while the prices of services increased by 3.4%.
This comes at a time when European Central Bank officials expect the inflation rate in the 19-nation European Union to reach 6.8% this year as a whole, before declining to 3.5% next year.