Odom was a main piece in a four-team swap that sent Clippers guard Mo Williams to Utah and also involved the Houston Rockets and Dallas Mavericks.
The deal returns Odom to the team that originally drafted him. He had enjoyed successful years with the Los Angeles Lakers, where he was the NBA Sixth Man of the year in 2010, before being traded last fall to the Mavericks.
Odom was a disappointment in Dallas and saw career lows in scoring and most other statistics. At the same time, he was involved in a reality television series with his wife, Khloe Kardashian, one of the famed Los Angeles Kardashian sisters.
Odom was expected to come off the Clippers bench again next season, the Los Angeles Times said Saturday.
The Times said the deal was consummated after Williams exercised an $8.5 million option on his contract and packed his bags for Utah.
The trade largely involved the rights to various draft choices. The Clippers sent the draft rights to Furkan Aldemir, the 53rd overall selection in this year's draft to Houston. The Jazz sent the draft rights of Tadija Dragicevic, Utah's second-round pick (53rd overall) in the 2008 draft to Dallas. And the Mavericks sent the draft rights of Shan Foster, a second-round selection (51st overall) in the 2008 draft, to the Jazz, with Houston also sending cash considerations to Dallas.