The execution was carried out after officials called for a speedy investigation and trial because of public outrage. The video emerged in early December and was later shown on state TV.
The two men, both 24, were convicted of "waging war against God", a broad charge that can cover actions ranging from anti-state organising to violent assaults.
The semi-official ISNA news agency said nearly 300 people witnessed the hangings.
ISNA said two accomplices received sentences that included 10 years in prison and 74 lashes each.