Team Melli defeated host Bosnia and Herzegovina in straight sets (26-24, 32-30, 25-12).
Defending champion Iran faced the home nation in the men's final, but stopped the crowd at Hotel Hills Arena from having much to cheer.
This is Iran's record eighth world title.
Between them, Iran and Bosnia and Herzegovina have won every world title since 1990.
Brazil earned the men's bronze medal, beating Egypt 25-21, 20-25, 25-23, 26-24.
In the women's final, Brazil won the world title with a hard-fought win over fellow first-time finalist Canada 3-2 (25-23, 18-25, 21-25, 25-17, 15-6).
The US won the bronze-medal match against Slovenia 25-8, 25-14, 25-10.
Both new world champions also qualify for the Paris 2024 Paralympics as a result of their victories.