After a free three-month trial, the subscription service will cost customers $9.99 per month to access the full library of songs.
Starting at a limit of 25 thousand songs, Apple wants to make 100,000 streaming songs available for iOS 9 users.
Apple is also launching Beats 1 on Tuesday. Featuring celebrity DJs who choose curated playlists, Beats repleases iTunes radio as a free service on Apple devices.
Apple Music will compete with services such as Rdio and Google Play Music, in addition to Spotify and Pandora.