The company, the Swedish offshoot of the international Three brand, is the first in Sweden to make the move, which is designed to help customers struggling to get 3G or 4G mobile coverage in some residential buildings, especially newbuilds.
It follows a number of complaints from Tre mobile users who have told the company that they are unable to get a decent signal at home.
"We know that there are Swedes who have problems with their indoor coverage and therefore we have worked intensively with both technology providers and handset manufacturers to launch Wi-Fi calls," the company's CEO in Sweden, Nicholas Högberg, said in a statement.
The new Wi-Fi offering will be free of charge for existing customers with fixed price contracts. However it will initially only be available to those using high-end models including the iPhone 5 and iPhone6, the Samsung Galaxy S6 and the Sony Xperia Z5.
The move comes after rival network TeliaSonera announced in January that it planned to improve its user experience by rolling out 5G wireless mobile technology from 2018. 5G offers faster speeds then 4G, making it easier for customers to download, stream and share photos and videos.
Sweden has long been a pioneering high technology nation and among EU member states, it is one of the leading countries for innovation. Sweden is also among Europe's top three spenders on research and development.