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 told ESPN's Adrian Wojnarowski.
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.
"Adding both size and depth to the wing position has been a goal, and the chance to accomplish that by acquiring a player with Rui's two-way skills and upside was an opportunity that doesn't present itself often," Lakers vice president of basketball operations and GM Rob Pelinka said in a statement.
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.
The deal will cost L.A. approximately $2.9 million in additional luxury tax this season if the team stays as currently constructed, according to ESPN NBA front office insider Bobby Marks.
Nunn was signed to the taxpayer's mid-level exception in the summer of 2021 and missed his entire first season with the Lakers because of injuries. He was in and out of the lineup this season because of inconsistent play, but had found a rhythm leading up to the trade, averaging 10.5 points on 47.4% shooting (35.3% from 3) in 11 games in January.
ESPN's Ramona Shelburne and Dave McMenamin contributed to this report.