ESPN reported the agreement on Saturday.
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Cousins averaged 16.3 points in 30 games with Golden State last season, one where he was dealing with recovery from a torn Achilles. He was also slowed in the playoffs by a quadriceps injury.
His Golden State Warriors teammate Quinn Cook is also reportedly headed to Los Angeles on a two-year deal.
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Cook tweeted the move with a tribute to his dad, who was a Laker fan.