The deal includes a 2023 second-round pick via Chicago, the Lakers' own in 2029 and the less favorable of the Wizards' and Lakers' 2028 second-round picks, sources said.
Hachimura, 24, had grown unhappy without a rookie contract extension in the preseason and became less of a priority with the emergence of Kyle Kuzma in the Wizards' frontcourt.
"I just want to be somewhere that wants me as a basketball player,'' Hachimura told reporters last week. "And I want to be somewhere that likes my game. ... I just want to be somewhere that believes in me and I can be myself. That's my goal.''
Los Angeles acquired Hachimura with the intention of signing him to an extension this summer, sources said. Hachimura can be a restricted free agent.
The Lakers believe that Hachimura gives them another sizable wing defender who has shown an ability to make corner 3-pointers and midrange shots when teams run the Lakers off the 3-point line. He has shot 40.8% on catch-and-shoot 3-pointers over the past two seasons, according to ESPN Stats & Information research, and is shooting 35.1% on catch-and-shoot 3s over the course of his career.
Hachimura, the ninth overall pick out of Gonzaga in the 2019 NBA draft, is averaging 13.0 points and 4.3 rebounds in 24.3 minutes per game this season.
Nunn, in his fourth NBA season, has played in 39 games this year after missing all of last season due to a knee injury. He was averaging 6.7 points off the bench for the Lakers this season.
ESPN's Ramona Shelburne contributed to this report.