Metallica's drummer Lars Ulrich said: "Our beef hasn't been with the concept of sharing music.
Metallica, who have been outspoken opponents of the free file-sharing service, will now have final say over which of their songs can be downloaded and which cannot.
The deals come a day after an American judge ordered the site to remain closed until it can prove that it has done everything in its power to make its system for blocking access to copyrighted material 100% effective.
The service, which has come under fire for offering songs without paying royalties to the artists, has been closed since the beginning of July.
Metallica's drummer Lars Ulrich said: "Our beef hasn't been with the concept of sharing music.
"The problem we had with Napster was that they never asked us or other artists if we wanted to participate in their business."
The issue has been resolved in a way "that works for fans, recording artists and songwriters alike," he said.
The band previously accused Napster of "hijacking" their music.
"Metallica has taken a courageous stand and a tough and principled approach to the protection of its name and creative output," Napster's chief executive Hank Barry said.
"They brought to our attention essential artists' rights issues which we've addressed in our new technology. We respect what they've done."
Metallica and Dr Dre agreed "to make certain of material available from time to time" once an acceptable system to ensure payment to artists and publishers is in place.
Hip-hop star Dr Dre said: "I work hard making music - that's how I earn a living.
"Now that Napster's agreed to respect that, I don't have any beef with them."
Dre and Ulrich have been two of Napster's highest-profile critics, but the service still faces pressure from the Recording Industry Association of America (RIAA).
The powerful industry group has vowed not to let up until Napster fully complies with copyright law.
Matt Oppenheim, RIAA vice president for business and legal affairs, said they would be happy to welcome Napster into the music market - if and when it is able to protect copyrighted works.
"Its never been our role to put Napster out of business," Oppenheim said.
"This has always been about protecting works that the owners wanted protected."