The law means that people travelling through Europe will be able to make and receive calls, send texts and browse the internet on their devices for the same price they pay at home.
Sunrise charges 100 francs for a similar roaming deal under its "Freedom" range, and offers add-on roaming bundles for pay-as-you-go travellers.
Luxembourg clients will now pay the same wherever they are in the 28-nation bloc as they do in the Grand-Duchy.
Consumers must be aware, however, that while the roam-like-at-home rules apply to services between mobile operators from one country within the whole of the European Union, they do not apply to foreign telecoms, experts have warned.
Anxious by the rise of eurosceptic parties in recent years, the European Union has seized upon the end of roaming to promote itself as a solution to Europe s problems, rather than a cause of them.
Today begins the roll out of the long-planned scrap of roaming charges across EU member states - something the European Commission has been working on for quite some time. This means that, if they notice that someone is using their SIM card mostly overseas and not in the country where the SIM card was bought, they may warn the user that they are about to start charging special charges for roaming because they suspect misuse.
But what does it mean for you?
If you have a top of the range tariff with unlimited data, you will find mobile operators have still put limits in place. In some countries, operators do not intend to control fair use in calls and text messages, but will in data traffic.More news: Key takeaways from Attorney General Sessions' testimony
Travellers are hoping that the new legislation will prevent hefty phone bills after trips overseas Why is there a ban on roaming charges?
If you have a data allowance of 2GB a month, for example, you will be able to continue to be connected and use email, browsers, social media, chat apps etc within the confines of this allowance - just like you could in the UK.
Although you can use your monthly allowance of data for no extra charge from anywhere in the European Union, most networks are imposing a "fair usage" policy, which caps your data allowance while you're away.
Have roaming charges been abolished?
Some operators will also cover countries in the European Economic Area or even further afield.
Holidaymakers are encouraged to check if their mobile provider includes Turkey in the ban or not, as this varies across the board.
It means that, while the United Kingdom is still part of the EU, Brits will also benefit from mobile roaming charges being dropped.
Under the new rules, roaming charges for calls, data usage and texts are no longer allowed. And will United Kingdom holiday-makers still be able to benefit from this after Brexit?