Radio Farda says Zamani was executed on 7 February. Iranian officials informed his family on 16 February and said they will return the body shortly.
Zamani, a member of Iran's main armed opposition group, the Mujahedin Khalq (MKO), was sentenced to death after being convicted in the 1998 bombing of a Tehran court. The blast killed three people and injured more than 20.
The vice president of the Paris-based International Federation of Human Rights, Abdolkarim Lahdji, said Zamani was not given the chance to defend himself adequately.
"This person was arrested on charges of being involved in a bombing operation, but unfortunately it is certain that this young man did not have a fair trial and was not able to defend himself. Secondly, we are against the death penalty even if it was proven in a fair trial that he was involved in a terrorist operation."
Radio Farda reported that the case has raised concern that more political prisoners could be executed.