The agreement is part of a broader set of measures to tackle financial crimes and tax evasion. EU legislators also backed stricter controls on pre-paid cards, and raised transparency requirements for the owners of trusts and companies.
"Today's agreement will bring more transparency to improve the prevention of money laundering and to cut off terrorist financing," Europe's Justice Commissioner Vera Jourova said.
The EU decision comes as bitcoin's prices have risen more than 1,700 percent since the start of the year, triggering worries that the market is a bubble that could burst in spectacular fashion.
The agreed measures will end anonymous transactions on virtual currency platforms and with pre-paid payment cards, which investigators said could have been used to fund attacks by militants.