T-Mobile and Google yesterday announced the official launch of Google Music. The service was originally announced at the company’s annual Google I/O conference in March.

The beta version of the service allowed users to upload their entire music library to the cloud for free. Now Google has added a new music store in Android Market that the company says is fully integrated with Google Music. The store offers more than 13 million tracks from various record labels.

T-Mobile said that one of the key aspects of Google Music is the service’s deep integration with Google+, Google’s social network.

“We believe Google Music will completely change the experience – allowing customers to not only discover and buy music in a new way, but also share their favorite tracks with friends on Google+,” T-Mobile said in a statement.

As the official launch partner of the service, T-Mobile is offering customers on smartphones and tablets running Android 2.2 and above free Google Music content from featured artists. Customers can download brand new tracks from Drake and Maroon 5.  Each week through the end of the year, T-Mobile will introduce new free tracks.

T-Mobile also said it will soon be offering carrier billing for music purchases.

Google Music is open for business in the U.S. at market.android.com, and over the next few days, the company will roll out the music store to Android Market on devices running Android 2.2 and above. Users can download the new music app from Android Market.