The Lakers announced the deal Thursday with Henry, who played for New Orleans last season.
The 6-foot-6 swingman appeared in 50 games for the then-Hornets, averaging 3.9 points and 1.8 rebounds.
The Kansas product was selected by Memphis with the 12th overall pick in 2010, and was traded to New Orleans in January 2012. He has started 18 games in his three-year NBA career.
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