The broadcaster confirmed a new app is available on the three streaming platforms at no extra charge to existing BT Sport customers.
It said that initially its three main sport channels as well as ESPN, Boxnation and BT Sport Extra will be offered as part of the service.
The launch of the app will make it possible for BT Sport users to access the service on their TV without the need for a set-top box, the company said.
Marc Allera, chief executive of BT’s consumer division, said: “We’re creating even more ways for our customers to watch their favourite sport in stunning high definition, wherever they are.
“We’re working to offer our customers unrivalled choice, with the best content, the smartest devices, and the latest technology, through partnerships with the world’s most innovative companies.
“Making BT Sport available on Apple TV, Samsung TVs and Xbox is just one of the ways we’re bringing great sport to even more customers, and creating the best sports viewing experiences in the UK.”