Mooar has been at the Super Rugby champions for three years and helped the Crusaders to a second straight Super Rugby title in 2018 alongside head coach Scott Robertson.
He was previously head coach of the Southland Stags as well as backs coach with South African sides Eastern Province Kings and Southern Kings in the Super 15.
The 44-year-old Mooar will join Scarlets in 2019, with Pivac taking over from Gatland as Wales coach at the end of next year's World Cup in Japan.
