The apparent breakthrough is likely to heighten international tensions over Iran's alleged pursuit of nuclear weapons, with the United States saying the move showed Iran was "moving in the wrong direction."
Making the announcement in a televised address on Tuesday, Mahmoud Ahmadinejad also said that Iran was determined to achieve enrichment on an industrial scale.
"I am officially announcing that Iran has joined the group of those countries which have nuclear technology. This is the result of the Iranian nation's resistance," Ahmadinejad said in the address from the northeastern city of Mashhad.
"Based on international regulations, we will continue our path until we achieve production of industrial-scale enrichment."
The announcement came shortly before Mohamed ElBaradei, the head of the United Nations' nuclear watchdog, was due to visit Iran for talks aimed at resolving an international standoff over its nuclear programme.
ElBaradei was expected to arrive in Tehran on Wednesday at the earliest.
The UN Security Council has demanded that Iran stop all nuclear enrichment processes by April 28, because of suspicions by several mainly Western countries that the programme is designed to develop nuclear weapons.
Apparently rejecting that call, Ahmadinejad said that the West must respect Iran's right to peaceful atomic technology.
"I am advising them to respect the Iranian nation's right to nuclear technology and not to create an ever-lasting hatred of themselves among our nation," Ahmadinejad said.
"We have repeatedly said that Iran does not need weapons of mass destruction."
His announcement came only hours after Akbar Hashemi Rafsanjani, a former president, disclosed that Iran was successfully producing enriched uranium.
"We operated the first unit which comprises 164 centrifuges, gas was injected, and we got the industrial output," Rafsanjani told Kuwait's KUNA news agnecy.
"There needs to be an expansion of operations if we are to have a complete industrial unit; tens of units are required to set up a uranium enrichment plant."
"I am officially announcing that Iran has joined the group of those countries which have nuclear technology"
Commenting on the Iranian claims, the Bush administration said the move showed "that Iran is moving in the wrong direction."
"Defiant statements and actions only further isolate the regime from the rest of the world," said Scott McClellan, the White House spokesman.
He added that if it persisted, America would discuss possible next steps with the UN Security Council.
The West fears that Iran could be using its nuclear power programme as a smokescreen to build atomic bombs, but Tehran denies this.
The International Atomic Energy Agency said last month that Iran had started testing 20 centrifuges.
Gholamreza Aghazadeh, the head of Iran's Atomic Energy Organisation, said in February that Iran had started work on uranium fuel, but using only a few centrifuges. He said then that Iran was months away from operating a full cascade.
Iran is accused of secretly
developing atomic bombs
On Tuesday, however, he confirmed the enrichment announcement.
"I am proud to announce that we have started enriching uranium to the 3.5% level," he said in a televised address.
He said that the pilot enrichment plant in Natanz, south of Tehran, had started working on Monday.
Each centrifuge chain contains 164 units. Such cascades refine uranium gas into fuel for power stations, or if highly enriched - to 90% - for bombs.
About 1,500 centrifuges running optimally for a year could yield enough material for a bomb, scientists say.