Napster, the music download site acquired by Best Buy Co. in 2008 for $121 million, now has a new home: Rhapsody International Inc.

Best Buy, No. 11 in the Internet Top 500 Guide, on Monday agreed to sell Napster to Rhapsody for an undisclosed amount. Under the terms of the agreement, Rhapsody will acquire Napster’s subscriber lists and certain other undisclosed assets. Best Buy will retain a minority stake in Rhapsody. The deal is expected to close in November.

With a bigger subscriber base, Rhapsody will be able to enhance its product line, the company says. “This deal will further extend Rhapsody’s lead over our competitors in the growing on-demand music market,” says Rhapsody president Jon Irwin. “There’s substantial value in bringing Napster’s subscribers and robust portfolio to Rhapsody as we execute on our strategy to expand our business via direct acquisition of members and distribution deals.”

Rhapsody, which houses a music download library of more than 13 million songs, is itself a relatively new company. For many years, Rhapsody was the online music arm of RealNetworks Inc. But in March 2010, RealNetworks spun off Rhapsody into a separate company that is jointly owned by RealNetworks and MTV Networks.

At the time of the spin-off, Rhapsody was generating annual sales of about $161 million, says RealNetworks. When Best Buy acquired it, Napster was generating annual sales of about $111 million. Rhapsody does not break out financials and Best Buy has not disclosed annual sales for Napster.

Best Buy is divesting Napster but becoming a minority owner of Rhapsody in part to get a bigger share of the download music market. “This is a ‘go big or go home’ business, so our focus is on sustainably growing the company,” says Irwin. Best Buy says Napster served a profitable niche. “Rhapsody has demonstrated that it has what it takes to build a profitable business in the increasingly competitive on-demand music market,” says Best Buy senior vice president and general manager of entertainment Chris Homeister. “We are confident they are the right partner to provide Napster’s existing subscriber base with an immersive digital music experience moving forward.”