Charlotte announced the move Tuesday, but did not release contract terms.
A person familiar with the situation had said the deal is worth $18 million over three seasons with a player option for the third season. The person spoke to The Associated Press on condition of anonymity because the details of the deal were not announced.
Henderson, selected by Charlotte with the 12th overall pick in the 2009 NBA draft, averaged a career-high 15.5 points and 2.6 assists last year, along with 3.7 rebounds. Henderson finished with 24 consecutive double-figure scoring games, the longest streak by a Bobcats player since the 2010-11 season.
He was second on the team in scoring last season behind only point guard Kemba Walker.