The service will be available on the Microsoft Lumia 640, plus the newly launched Galaxy S6 and S6 Edge (seen above), with other handsets to follow. According to a post on the company site, wi-fi calling for the iPhone 6 and 6 Plus is also planned, with the iPhone 5s and 5c to follow, with the aim of having these users connected users by summer.
According to EE, one in ten people have one or more rooms in their homes where they have no mobile signal, often a problem exacerbated in rural areas. But by piggybacking on their home or other wi-fi, users can still make calls in their mobile not-spots.
EE's service, which utilises the IP multimedia subsystem framework, was launched at an event in the Churchill War Rooms underneath Whitehall: despite the underground location (and a five foot thick concrete shield above it) it was possible to make phonecalls over a wi-fi connection using the service.
Of course, being able to make calls in without a mobile signal may not be welcomed by everyone - there are already few places where people can escape from a ringing phone and EE's service will reduce them further.
For example, I tested EE's wi-fi calling on the London Underground (Virgin Media provides a wi-fi network on the underground) which made it perfectly possible to make a call while on a train on a platform, although it cut off when the train went into the tunnel and the wi-fi signal dropped.
Mobile operators are competing with a number of popular apps which offer calls from smartphones using voice over IP such as Skype, Apple's Facetime, Viber, and most recently WhatsApp.
EE argues that its service is easier to use than such apps, as it uses the phone's standard dialler and contacts - users don't need to have a special app or ensure their friends are using the same service.
The company said that by summer, five million EE pay monthly customers will have access to the wi-fi calling service, when it will also become available to corporate customers. EE had initially planned to launch the wi-fi calling system last autumn but it was then delayed because of the complexities involved - for example, the service can be used to make an emergency call which is not the case with some other IP-based phone services.
EE is not alone in exploring calls over wi-fi: last month Vodafone also said it plans to launch a similar service in the summer. O2 currently has an app called Tu Go which allows users to make calls over wi-fi, while Three has one called Three InTouch, where calls and texts come from the subscribers monthly price plan or pay-as-you-go credit.