The explosions, which took place in the city of Ahwaz, in the province of Khuzestan, killed at least six people and wounded around 100. The two bombs went off in a shopping center.
Although a number of foreign-based Arab groups claimed responsibility, no definite information about who exactly carried out the attack ever emerged.
The Iranian government accused groups with links to foreign states, including the U.K., of planning the bombings after Iran was hit by a series of bomb attacks around the country in 2005-06.
Although it is not known exactly how many people were arrested in connection with the attacks, more executions are likely.
"A number of criminals are awaiting the death sentence in connection with the bombings," the city's public prosecutor said after the executions.