The 7-foot Mihm, who left Texas after his junior year, was drafted by Chicago, then traded to Cleveland minutes later for No. 8 pick Jamal Crawford and an unspecified amount of cash.
Under the NBA's rookie salary scale, Mihm will receive within 20 percent of about $5.17 million over three seasons.
Mihm averaged 17.7 points and 10.5 rebounds last season for the Longhorns.
"We're thrilled that Chris has signed," general manager Jim Paxson said. "We're delighted that Chris will participate on our summer league team during the Rocky Mountain Revue and that he'll get a head start working with our coaching staff."
Cleveland needed size with injury-prone 7-3 center Zydrunas Ilgauskas' status uncertain.
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