The Suns receive forward Darrell Arthur in return, but are expected to waive Arthur following a contract buyout. Arthur is due $7.4 million for the upcoming season.
The second-round pick is for 2021 and reportedly is protected through No. 35, the latest in a haul of draft picks collected by the Nets.
Dudley, 33, joins his sixth team as he heads into his 13th season. He's a career .396 shooter from beyond the arc and has averaged 8.0 points, 3.3 rebounds and 1.6 assists over 788 career games.
He's due $9.5 million this season.
Arthur, 30, has averaged 6.5 points and 3.5 rebounds in 503 career games with Memphis and Denver.
--Field Level Media