The cloud-based service offers streaming of more than 30 million songs on PC, laptop and tablet devices running Windows 8 and Windows RT, including Microsoft's own Surface line of tablets, along with the Xbox 360 console and Windows Phone 8 smartphones.
Alongside a free streaming service supported by adverts, Xbox Music also has a music subscription pass for unlimited playback of tracks, both online or offline, and an iTunes-style music store.
Microsoft feels that digital music is currently too hard to manage across multiple devices, and so it has created Xbox Music as a service offering "immediate and comprehensive discovery across the different types of devices you own".
Users of Windows 8 or Windows RT tablets and PCs can stream tens of millions of songs for free, supported by adverts, as well as create an unlimited amount of playlists. However, Microsoft said that it will limit the amount of free streaming after the first six months.
Users can instead opt for the Xbox Music Pass, giving them unlimited access to the songs without adverts on Windows 8 devices, along with Xbox 360 and Windows Phone 8 smartphones, including while offline. This costs £8.99 a month and also includes a range of music videos on the Xbox 360.
Also launching is Smart DJ, an artist-based radio feature that offers personalised and off-the-peg playlists of music based around favourite artists or genres.
The Xbox Music Store is an MP3 marketplace offering single tracks or entire albums for purchase on Windows 8, Windows RT and Windows Phone 8 devices.
As Xbox Music is based around cloud technology, Xbox Music Pass subscribers can create playlists and then have them synced across all their compatible devices.
Microsoft will also soon launch an iTunes Match-style service that allows the user to upload their music collection to the cloud and any available tracks will be replaced with better versions from the Xbox Music catalogue.
"The launch of Xbox Music is a milestone in simplifying digital music on every type of device and on a global scale," said Don Mattrick, the president of the Interactive Entertainment Business at Microsoft.
"We're breaking down the walls that fracture your music experiences today to ensure that music is better and integrated across the screens that you care about most - your tablet, PC, phone and TV."
Free Xbox Music streaming launches on Windows 8 and Windows RT tablets and PCs on October 26 in 15 markets worldwide.
Xbox Music Pass will be available for Windows 8, Windows RT and Windows Phone 8 in 22 markets worldwide as devices become available, but it will begin rolling out tomorrow (October 16) on Xbox 360 in the same markets.
Xbox Music Store will also be accessible on Windows 8, Windows RT and Windows Phone 8 in 22 markets worldwide as devices become available.
Microsoft said that it will continue introducing Xbox Music in new regions around the world throughout the coming year.
It is also in talks to expand the platform, although it is unclear whether that will include rival operating systems such as Apple's iOS and Google Android.
Microsoft told The Verge that existing Windows Phone and Windows 7 users will not get access to Xbox Music, but instead continue to use the Zune Music service, which will give access to the same catalogue of songs as Xbox Music.