"I wish the other three members nothing but the best in all of their future endeavors," Cornell said Thursday in a statement.
An after-hours call to Audioslave's music label was not immediately returned.
Cornell, 42, a former singer and guitarist with Seattle grunge band Soundgarden, said he'll release a solo album May 1 called "Carry On." He also co-owns a restaurant in Paris, where he splits his time.
Audioslave was formed in 2001 and comprised of Cornell and three former members of Rage Against the Machine. The group recorded three albums and performed in Havana in 2005.
Meanwhile, Rage Against the Machine planned to reunite to perform at this year's Coachella Valley Arts and Music Festival, which runs April 27 through 29. Tom Morello, the lead guitarist of Rage Against the Machine and Audioslave, has said the concert is a one-shot deal.
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