"With this launch, the Islamic Republic of Iran has officially achieved a presence in space," Mahmoud Ahmadinejad, the Iranian president, said in a broadcast.
Omid will stay in orbit for up to three months as part of a programme Iranian officials say is aimed at improving telecommunications and monitoring natural disasters.
Ahmadinejad has made scientific development, which often puts Iran at odds with the West, a central theme of his presidency.
The satellite's launch demonstrates the development of technologies that many countries fear could one day be used to launch nuclear weapons. Iran insists it has no plans to do so.
The Iranian Fars state news agency said the satellite "has been designed for gathering information and for testing equipment ... [that] is going to help Iranian experts send an operational satellite into space".
It said the launch was "another achievement for Iranian scientists under sanctions".
Iran is under two rounds of UN sanctions due to its refusal to halt uranium enrichment, which the US and other Western nations fear could lead to the production of nuclear weapons.
Tehran says its nuclear ambitions are limited to generating electricity.
A satellite was put into orbit by Iran in 2005, but was carried by a Russian rocket.