The sanctions ban the supply of nuclear-related technology and materials and impose an asset freeze on key individuals and companies.
The US representative warned that Iran’s pursuit of nuclear weapons would make it less, not more, secure.
Iran says its programme is for peaceful purposes and has vowed to continue.
The draft resolutionn was amended several times after objections from both the Russians and Chinese.
But after parts of the resolution were watered down, both Russia and China – who have close financial ties with Iran – backed the proposals, which were passed by the 15-member council.
The resolution, under Chapter Seven of Article 41 of the UN Charter, makes enforcement obligatory but limits action to non-military measures.
But acting US ambassador to the UN, Alejandro Wolff, said the resolution sent a strong warning that there would be serious repercussions to Iran’s continued defiance of the international community.
“Today we are placing Iran in the small category of states under Security Council sanctions,” Mr Wolff said.
“If necessary, we will not hesitate to return to this body if Iran does not take further steps to comply.”
Iran’s foreign ministry spokesman, Mohammad Ali Hosseini, condemned the resolution as illegal.
He told state-run television that the decision “cannot affect or limit Iran’s peaceful nuclear activities but will discredit the decisions of the Security Council, whose power is deteriorating.”
The resolution, which demands that Tehran end all uranium enrichment work – which can produce fuel for nuclear plants as well as bombs – was the result of months of protracted negotiations.
Hours before the vote, US President George W Bush spoke to Russia’s Vladimir Putin and discussed the issue, agreeing on the importance of a unified stance.
In a statement before the Security Council, Russia’s ambassador to the UN, Vitaly Churkin, emphasised that the resolution did not authorise the use of force.
But he said the sanctions sent a “strong message” to Iran about the need to comply with the UN’s nuclear watchdog, the International Atomic Energy Agency (IAEA).
The text was watered down to take account of Russian concerns over such provisions as a freeze on the assets abroad of specific Iranian individuals and organisations.
Russia is building a nuclear power station Iran and China has significant oil interests there.
The resolution demands that Tehran end all uranium enrichment work, which can produce fuel for nuclear plants as well as for bombs.
Iranian President Mahmoud Ahmadinejad has threatened to reconsider relations with those countries which support sanctions. BBC