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Napier, 24, was the 24th overall pick in the 2014 NBA draft by the Charlotte Hornets and was traded to Miami in a draft-day deal. He averaged 5.1 points, 2.5 assists and 2.2 rebounds in 51 games for the Heat last season.
The Heat traded Napier, who will make $1.3 million in 2015-16, to reduce their luxury tax bill.
He helped lead Connecticut to the national title in 2014 and was the Final Four Most Outstanding player.