Henry, 23, played well for the Lakers before surgery for a torn ligament in his left wrist cut his season short in April.
Henry averaged 10 points in 43 games for the Lakers, who have refurbished the roster with players on short deals to keep open salary-cap space for the future pursuit of star free agents.
Besides Henry, the Lakers have retained free agents Jordan Hill and Nick Young and added forwards Carlos Boozer (amnesty waiver claim) and Ed Davis. The Lakers acquired guard Jeremy Lin in a trade with Houston, and drafted forward Julius Randle of Kentucky.
Henry was the 12th overall pick by the Memphis Grizzlies in the 2010 NBA draft. He played sparingly for the Grizzlies for one season before a trade to New Orleans, where he played a reserve role in the next two years. The Lakers signed him as a free agent in September 2013.
The Lakers plan to place guard Kendall Marshall on waivers, but have a strong interest in re-signing him to a new deal should he go unclaimed in the waiver process, league sources told Yahoo Sports.
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