Bucker will replace Serbian Nibucha Moscovich as Ahli coach next season after the latter’s negotiations with the Jeddah-based club reached a dead end.
Al-Watan newspaper revealed a one-year-deal worth $450,000 for the former Ismaili coach, which means more than double his salary at Wehda.
The move was expected after the Saudi club announced their interest in the German over the recent weeks.
Bucker led Wehda to a historic third place in the Saudi league this season, reaching the final-four stage for the first time.
Former Al-Hilal Portuguese coach Jose Peseiro was short listed for the job as well, but Bucker was preferred after his exploits with Wehda.
Ahli clinched a cup double this season, winning the Saudi Cup and the Saudi Crown Prince Cup, but their fifth league position was considered a huge disappointment.