The decision, "paves the way for EU Internet users for the first time to be able to have pan-European domain names and e-mail addresses", said European commissioner for the Information Society, Erkki Liikanen.
The European parliament gave its blessing to the project last month and the European Commission, the initiator of the .eu project, will now push ahead in setting up the infrastructure needed for the domain.
This includes selecting of a private, non-profit organisation to manage the TLD, and defining rules to prevent domain-name squatting and to ensure effective cross-border settlement of disputes about domain names.
The Commission is expected shortly to call for organisations interested in running the .eu registry to step forward.
National registries within the EU are expected to be among the likely candidates. The Irish registry, which manages the .ie domain, has so far expressed the most interest.