The deal, for an undiclosed sum, will see Rhapsody launch in the UK and Germany under the Napster brand name. Rhapsody has existed in the US for 11 years and has more than one million paying customers.
Last October Rhapsody bought Napster's US business, which it then re-structured. It says it intends to keep all Napster International's staff and migrate existing users to its infrastructure in March.
The Napster name will be retained in the UK and Germany because it is better known in Europe than Rhapsody.
"The acquisition of Napster and its subscriber base in the UK and Germany gives us an ideal entry to the European market," says Rhapsody president, Jon Irwin.
Arch-rival Spotify launched in the US last July, and is already well established in Europe. It has 2.5 million paying subscribers.