The new rules, which came into force on Thursday, mean that citizens travelling within the EU will be able to call, text and browse the internet on mobile devices at the same price they pay at home.
In a statement, the Commission said, "Each time a European citizen crossed an EU border, be it for holidays, work, studies or just for a day, they had to worry about using their mobile phones and a high phone bill from the roaming charges when they came home."
It had been working hard over the last 10 years to fix this "market failure", it said.
"Eliminating roaming charges is one of the greatest and most tangible successes of the EU," the Commission added.
Spanish MEP Pilar Del Castillo Vera, who negotiated the historic agreement on behalf of Parliament, agreed, saying, "The elimination of roaming charges for voice calls, text messages and data is an initiative by the Parliament that benefits more than 500 million consumers as well as Europe's SMEs and start-ups in all sectors of the economy.
"The strong commitment and political leadership of the European Parliament has been crucial for abolishing roaming charges."
Del Castillo Vera added, "Beyond the tangible savings for consumers, the abolishment of roaming charges represents the end of another barrier to the free circulation of people and services inside the EU. It is a very good example of the EU's added value. Our capacity to achieve concrete results such as this strengthens the European project."
She also said, "The end of roaming is an important step in the development of the digital single market, one of the European institutions' priorities for this legislature."
But a UK consumer group warned phone users could face "unexpected charges".
Exceeding agreed minutes, texts and data would still be charged in the EU as it would in the UK, with providers charging different rates, said Which?
In addition, different providers included different countries in their roaming territories, such as the Channel Islands and Switzerland.
Which? said mobile users should check the detail of their tariffs with their phone providers to avoid being caught out by surprise charges. Until now roaming, or connection, charges have been added to the cost of calls, texts and internet browsing when consumers from one EU country travelled to another and connected to a mobile network there.
In some cases, mobile users have faced bills of hundreds of euros if, for example, they have downloaded a film.