The company already offers its TV customers access to around 2,500 current and back catalogue music videos and concerts.
From today users can also stream individual tracks or whole albums from acts signed to Universal Music.
All tracks are advert-free and BT says it hopes to add more labels to the service in the coming months.
The new Music bolt-on is included in existing TV Unlimited customers’ subscriptions and new TV customers can add it for £3 a month.
Alex Green, director of BT TV, said: “We are really excited to have signed this contract with Universal Music and we are hopeful we can sign other deals with more labels in the near future.
“This takes our Music offering to another level, at no additional cost to customers. It will allow them to enjoy a whole album at times when they are not necessarily able to sit down and watch the TV.”