The 30-year-old gets a one-year, $2.3 million contract, according to his agent, Joel Bell. The deal was first reported by The Vertical.
Cunningham declined a $3.1 million player option to seek a multiyear deal.
The versatile forward was the Pelicans' top 3-point shooter at a career-high 39.2 percent during the 2016-17 campaign after making only two 3s in his first six years in the league from 2009-10 to 2014-15. He averaged 6.6 points and 4.2 rebounds per game this season while shooting 48.5 percent from the field.
In NBA circles, Cunningham is considered a veteran glue guy and a stable locker room presence.
The eight-year forward has also had stints with Portland, Charlotte, Memphis and Minnesota throughout his career.
ESPN's Bobby Marks and Royce Young contributed to this report.