The deal is subject to the approval of the US bankruptcy court overseeing Napster's assets. The court is expected to rule on the deal by 27 November.
Napster was effectively shut down in July 2001 after record industry heavyweights took the company to court for infringing copyright laws.
Napster had been the subject of a number of bids, including one from Spanish porn consortium, the Private Media Group.
Roxio, which makes CD burning applications, offered to pay US$5 million in cash, as well as 100,000 share warrants to purchase Napster's assets.
Shares of Roxio jumped 10 percent in US trading following the news.
