The ministers support, which was widely expected after the European Parliament voted in favour of the price caps last month, paves the wave for the new rules to go into effect in the coming months.
Member states still have to formally adopt the new rules on June 25 and then they have to be officially published on June 29, according to estimates from the EU's Germany presidency.
However, consumers are unlikely to benefit before September because operators will have a month after the new rules take effect to make new offers to customers and then another month to change clients contracts.
"I'm glad for European consumers because today is a big day, finally roaming will be wrapped up," said German Economy Minister Michael Glos as he arrived to chair the meeting.
The European Commission first drew up proposals to regulate so-called roaming rates last year after finding evidence of huge variations between operators' prices, with some roaming calls costing up to six times those of local mobile calls.