The person, who spoke on condition of anonymity to The Associated Press because teams can't confirm moves until the new league year begins Wednesday, also said Milwaukee has the right to swap 2018 second-round picks.
"Just landed in Cameroon and got told I've been traded to Sacramento!!" Mbah a Moute wrote on his Twitter page.
The 6-foot-8, 230-pound forward has emerged as a standout defender since he was drafted 37th overall out of UCLA by the Bucks in 2008. He has averaged 6.9 points and 5.3 rebounds in 25.1 minutes per game in his career.
CBS Sports first reported the trade.
Mbah a Moute has two years left on a four-year deal worth about $19 million that he signed as a restricted free agent before the lockout-shorted 2011-12 season. That move came when Milwaukee matched the offer sheet from Denver, where new Kings general manager Pete D'Alessandro worked in the front office at the time.
In Sacramento, he will be expected to fill the void at small forward. The Kings made an attempt to sign Andre Iguodala at that spot before he landed a four-year, $48 million deal with the Golden State Warriors last week.
Mbah a Moute will compete with incumbent starter John Salmons for playing time. The Kings will likely still explore other opportunities in free agency.
Also Tuesday, new coach Mike Malone was busy filling out his coaching staff.
Dee Brown, a 12-year NBA veteran and 1991 slam dunk champion, was hired as assistant coach and director of player development. Micah Nori and Bill Pope also were hired as assistants.
The trio joins lead assistant coach Chris Jent and Brendan Malone on Sacramento's bench.