Xbox Music will become available on Xbox 360 games consoles from Tuesday.
It will become available on Windows-based devices after the launch of Windows 8 towards the end of the month.
The service replaces Microsoft's Zune media service, which was discontinued in June.
With a database of about 30 million songs, the Xbox Music catalogue is larger than that of Apple's iTunes, which has more than 26 million individual tracks.
The free version of the service will enable users to stream music, with adverts appearing every 15 minutes.
"As an entertainment company, music is an important ingredient on its own and as a part of different user experiences," said Xbox Music general manager Jerry Johnson.
Mr Johnson added that research carried out by Microsoft 18 months ago suggested that Xbox owners spent 60% of their time on the console using entertainment services rather than playing video games.
Film service Netflix, BBC iPlayer and sports TV network ESPN are all available via the Xbox console.