The Lakers announced the deal Friday.
Henry averaged career highs with 10.0 points, 2.7 rebounds and 1.2 assists in the swingman's first season with the Lakers despite numerous injuries that limited him to 43 games.
The four-year NBA veteran underwent surgery on his left wrist and right knee after his season ended, and his recovery from the injuries likely affected his ability to land a bigger free-agent contract.
Henry was the 12th overall pick in the 2010 draft by Memphis. He also played two seasons with New Orleans before joining Los Angeles as a training-camp invitee last year.