US Secretary of State Colin Powell said the resolution would be "forward-looking" and would "not fight the battles of the past" - a reference to the bitter divisions in the council before the US-led invasion of Iraq.
The BBC's Jon Leyne in Washington says Russia and some other council members are reluctant to relinquish their control over Iraq's oil, exercised under the sanctions regime.
Earlier, the United States announced that it was lifting some of its own economic sanctions against Iraq, with immediate effect.
Primary among them are rules which will allow the thousands of Iraqis resident in the US to send up to $500 a month to family and friends in Iraq.
With the economy in ruins after a decade of sanctions, and the aftermath of the war causing yet further hardship, access to hard currency is necessary to acquire many basic commodities, exiled Iraqis told BBC News Online.
US Treasury Secretary John Snow said the move was an "essential step" to allow reconstruction to begin.
"The regime that was once the target of our economic sanctions has been extinguished, and our mission now is to rebuild Iraq," he said.
permitting privately funded humanitarian activities by US-based organisations.
However, restrictions on the export of goods which are controlled for national security purposes will remain, with a special government license being required for such trade.
The thousands upon thousands of Iraqis resident outside their home country have struggled ever since sanctions were imposed in 1991 to get money to loved ones back home.
Rubar Sandi, chairman of the US-Iraq Business Council in Washington DC, has been sending money to relatives for years - and has been among those who have led the lobbying to allow remittances and humanitarian assistance.
"This is the most fantastic news," he told BBC News Online shortly after the announcement."
"We've been pushing for this for a long time, so we can get to work back in Iraq."
He and his colleagues were trying to convince US Treasury officials of the need for these moves earlier this week, he said.
His organisation, he added, can now get on with establishing offices to promote humanitarian activity in Iraq - impossible till the announcement was made, given the need for massive amounts of money for premises, security and supplies.
No legal route
Till now, Mr Sandi told BBC News Online, the only options have been illegal.
One way has been through taking cash in person - up to the $10,000 limit imposed on all travellers leaving the US.
Another is to lodge money in Jordanian bank accounts and get couriers to take it into Iraq, or to do the same through Turkey and Iraqi Kurdistan.
A third is the hawala route, where informal money-brokers take money in the US and get contacts in Iraq to deliver the equivalent - minus a fee, of course - to recipients there.
This is identical to the hawala, or hundi, system prevalent across the Middle East and South Asia, but which has been widely used by extremist groups - including, ahead of 11 September 2001, al-Qaeda.
The US is keen to crack down on hawala, and is eager to reduce the need for it in Iraq.
Ahead of the game
Because of this, official money brokers are likely to move in relatively quickly.
But non-US companies are worried that Western Union, by some way the market leader, will have an advantage as a US firm.
Chequepoint, a UK operator, is lobbying the UK Government to make sure Western Union or any other outfit does not manage to secure a de facto monopoly, as it has in some parts of the Balkans.
Now that sanctions are being lifted, the way is clear for the US to hire consultants to rebuild Iraq's currency and financial system.
Sources in Washington told BBC News Online that BearingPoint, the successor to KPMG Consulting, is likely to get the deal, which could be worth up to $70m.
BearingPoint already has a three-year $40m contract to do the same in Afghanistan.