Crusaders first-five Mo'unga will be joined by Highlanders and All Blacks flanker Shannon Frizell at the club, who are coached by ex-New Zealand captain Todd Blackadder.
Mo'unga (28), who has 44 All Blacks caps, had signed a three-year deal with Toshiba.
Under New Zealand Rugby rules, Mo'unga and Frizell will not be eligible to play for the All Blacks while in Japan. The duo are set to join the club after next year's Rugby World Cup in France.
The Tongan-born Frizell (28) has made 25 appearances for the All Blacks and played 57 games for the Highlanders since his debut in 2018.
Mo'unga, who played 94 games for the Crusaders and scored more than 1,000 points, said he was looking forward to experiencing rugby with an overseas team.
"I'm grateful for this opportunity and to be part of the Lupus family I plan on doing everything I can to make Toshiba Brave Lupus Tokyo the number one team in Japan," he said in the media release.
"It's a dream of mine to play rugby overseas and to experience a different culture and I know this will be an amazing experience for my family."