The Kiwi will replace former coach Glen Jackson on a two-year deal at the Super Rugby Pacific outfit.
He was part of Scott Robertson's staff that helped the Crusaders to three-straight titles, before joining Welsh club Scarlets in 2019 and helping Scotland's 2023 World Cup campaign.
He then returned to Christchurch as an assistant to claim another title last year.
The Drua were admitted to the competition in 2022 and have battled for consistency, while regularly losing top talent to rival clubs.
They beat the ACT Brumbies twice this year - including in Canberra - on the way to five wins and a second-last placed finish, ahead of only Moana Pasifika, who have since been removed from the competition.
"What drew me to this role is the chance to work with such wonderful athletes, to be part of a culture and a people I deeply admire, and to help build something meaningful for the nation," Mooar said.
"I believe there are enormous opportunities for us to play a special brand of rugby that is successful, entertaining and inspiring.
"We want to inspire the country, win championships and continue to grow our people and the game in Fiji by creating something the country can be truly proud of."
Fijian Drua CEO Jeff Miller described it as "one of the most important appointments in the short history" of the club.
"We were determined to conduct a genuinely exhaustive process," he said.
"We received applications from an outstanding group of coaches and were extremely impressed by the quality, experience and different perspectives presented throughout the process.Â
"Brad stood out through his technical and tactical knowledge, his experience in championship-winning environments, his understanding of player development and, importantly, his ability to build strong relationships.
"He has coached at the highest levels of the game, has led his own professional programme and understands what is required to develop a clear Fijian rugby identity and create a consistently successful high-performance environment."
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