Al Qadsiah, whose squad includes Italian striker Mateo Retegui and former Real Madrid defender Nacho, is in fifth place in the Saudi Pro League in their first season after promotion.
Rodgers departed Celtic on Oct. 27 under a cloud, his second spell in charge damaged by scathing criticism from major shareholder Dermot Desmond that Rodgers' conduct had been "divisive, misleading, and self-serving" and that he "contributed to a toxic atmosphere around the club."
He has opted to continue his managerial career outside Britain for the first time, having previously coached Liverpool, Leicester and Swansea.
In its statement announcing the hiring of Rodgers on Tuesday, Al Qadsiah described him as a "world-renowned coach" and said his arrival "reflects the club's ambitious vision and its rapidly growing sporting project."
Aramco, the state-owned Saudi oil giant, bought Al Qadsiah in 2023 in a move that has helped to transform the club's status.
"This is a landmark moment for the club," Al Qadsiah chief executive James Bisgrove said. "The caliber of his experience and track record of winning reflects our ambition and long-term vision to establish Al Qadsiah as one of Asia's leading clubs."
Rodgers is coming off winning back-to-back Scottish league titles with Celtic, where he won 11 major trophies across his two spells. He also won the FA Cup with Leicester.
Al Qadsiah's last two managers were former Liverpool striker Robbie Fowler and former Spain midfielder Michel.
