Do Americans need permission to travel to Iran from the U.S. government?
No. Iran is not like Cuba or some other countries, for which you need permission from the U.S. Treasury Department to visit. There are absolutely no restriction at all for visiting Iran.
There is a U.S. State Dept. travel warning for Iran, which you might want to read. These warnings often serve a political purpose and do not necessarily indicate any danger.
http://travel.state.gov/content/passports/english/alertswarnings/iran-travel-warning.html