Gholam Reza Aghazadeh, the Iranian vice-president and head of Iran's nuclear programme, told Iran's state news agency that the plant would begin generating electricity within the next six months.
Russia is assisting Iran in the construction of the Bushehr plant, in southern Iran, in a $1bn contract, though Iran has complained of delays.
Russia attributed the delays to payment disputes, although analysts say it was unhappy with Iran's resistance to international pressure to make its nuclear programme more transparent.
Iran says its nuclear programmes are purely for peaceful purposes. However, the West has accused it of attempting to develop nuclear weapons.
'New conditions'
The Russian foreign ministry said in a statement that the fuel was delivered under the control and guarantees of the UN's nuclear watchdog, the International Atomic Energy Agency - which has approved the shipments.
It also said Iran had guaranteed the fuel would be used only for the Bushehr power plant.
"We believe qualitatively new conditions have been created which will allow Iran to take the steps which are demanded of it ... for the restoration of trust in the peaceful nature of the Iranian nuclear programme," it said.
Russia has resisted attempts by the West to impose harsher sanctions on the Islamic Republic.
However, it has also repeatedly urged Tehran to co-operate with the IAEA to resolve concerns over the programme.
'No reason'

"If the Iranians accept that uranium for a civilian nuclear power plant, then there's no need for them to learn how to enrich"

George Bush, US president

George Bush, the US president, said he approved of the shipment, but warned Iran that the move meant there was no need for them to continue enrichment.
"If the Russians are willing to do that [shipment], which I support, then the Iranians do not need to learn how to enrich," he said.
"If the Iranians accept that uranium for a civilian nuclear power plant, then there's no need for them to learn how to enrich."
Israel criticised the Russian decision, saying there was "no doubt" that the uranium was not meant "for peaceful energy or nuclear industry", Avigdor Lieberman, Israel's minister for strategic affairs, told Israeli parliament.
"There is no explanation for the uranium enrichment other than a will to obtain a nuclear weapon."
Israel is particularly concerned about Iran's nuclear programme after comments made by the Iranian president, Mahmoud Ahmadinejad, calling for Israel to be "wiped off the map".
It has also criticised a recent US intelligence report which concluded that Iran abandoned its nuclear programme in 2003.