The contract will pay Mueller $1.5 million this season and $2.5 million next year, sources told ESPN's Pierre LeBrun.
Mueller, 22, was acquired by the Avs from the Phoenix Coyotes at the trade deadline on March 3. He had nine goals and 11 assists 15 games with the Avalanche. He scored in each of his first seven games with Colorado.
Mueller missed the final four games of the regular season and the playoffs because of a head injury suffered on April 4.