New Zealand's 2015 World Cup-winning coach Steve Hansen has been part of Toyota's setup since 2019 as their director of rugby but will also serve as head coach for the upcoming season.
Glasgow announced earlier this month that Gray would be leaving his boyhood club for the second and last time at the end of November to take up a playing opportunity overseas.
The 35-year-old's new team-mates will include South Africa flanker Pieter-Steph du Toit, New Zealand's Beauden Barrett and Aaron Smith as well as high-profile rugby league convert Joseph Manu.
Toyota kick off their 2024-2025 season away against former League One champions Kubota Spears on Sunday 22 December at Chichibunomiya Rugby Stadium in Tokyo.