The move is designed to benefit people who may be abroad on holiday, for studies or for business.
At present, consumers visiting another EU country often cannot access and use online content services, such as music, games, films, entertainment programmes or sporting events, that they have subscribed to in their home country.
This is because their cross-border portability is restricted by territorial and exclusive licensing practices.
The new rules will remove these restrictions for all new subscriptions and also for those purchased before the rules enter into force.
However, they will apply only to online fee-based services.
Free-of-charge services will not be subject to the rules, but their providers will have the option of making them portable EU-wide.
According to the Commission, almost half of EU internet users, 49 per cent, listen to music, watch videos and play games online.
Many of them expect to do so while they travel in the EU. Their numbers are expected to grow as Europeans will pay less to access the internet on their mobile devices in other EU member states from 15 June 2017, when mobile roaming charges end in the bloc.
The new rules now need to be formally approved by Parliament and Council.
They were welcomed by Parliament’s rapporteur on the dossier, French ALDE group member Jean-Marie Cavada.
He said, "The quality of the discussions between the institutions has led to this satisfying agreement that will benefit all EU-citizens but also service providers, right holders and creators. This signifies very important progress in the context of the single market."
Further comment came from UK ECR group member Daniel Dalton, who said, "I always found it bizarre that consumers buying an online sports or entertainment package in the UK found themselves geo-blocked when they went on holiday.
"The new proposals will end this anomaly. Every study shows that accessing sport and services like Netflix is growing every month and the current laws were simply outdated. This is not just a victory for the consumer but a win for common sense."