The resolution, agreed on Thursday, says the deployment would only take place with the agreement of the Sudanese government, which remains opposed to UN intervention.
Twelve of the security council's 15 members approved the joint US-British resolution, while China, Russia and Qatar abstained.
The UN troops are set to take over from an African Union peacekeeping force in Darfur, which has been unable to prevent the widespread killing of civilians.
The mandate of the poorly equipped AU force runs out at the end of September.
In Washington, Kristen Silverberg, a senior state department official, said that Khartoum's agreement was not needed to reinforce the UN mission in Sudan.
"The resolution invites Sudanese consent; nothing requires Sudanese consent," she said.
Osman Yusuf Kibir, the governor of North Darfur, said on Sudanese television: "The resolution lacks legitimacy and credibility.
"The resolution was based on the premise that security is deteriorating in Darfur. This is a false assumption as security has improved and prevails all over the region."
The official SUNA news agency quoted al-Bashir's government as saying: "The Sudanese people will not consent to any resolution that will violate its sovereignty."
Deploying UN peacekeepers is seen as crucial to the success of a fragile Darfur peace agreement signed by Khartoum and the main Darfur rebel faction in May.
Although the security council cannot take significant action on the resolution until Sudan reverses its opposition to a UN force, the US and Britain, the two original sponsors of the resolution, hope the vote will help put new pressure on Omar al-Bashir, the Sudanese president, to acquiesce.
Millions of Sudanese have been
displaced during the conflict
The US ambassador to the UN, John Bolton, said the resolution was imperative "to stop the tragic events unfolding in Darfur".
"Every day we delay only adds to the suffering of the Sudanese people and extends the genocide," he said.
China and Russia said they supported the contents of the resolution but wanted Sudan's consent before adopting it.
Wang Guangya, the UN ambassador to China, said that by pushing ahead the council only risked triggering further violence in Darfur.
"This is obviously not the intended outcome of the council in adopting this resolution," he said.
The resolution would place peacekeeping authority for the Darfur mission into the hands of a separate UN force already deployed in Sudan's south.
That force, which has about 10,000 troops, would be expanded to 17,000 military personnel and up to 3,300 civilian police to cover both areas.
More than 200,000 people have died in Darfur region since 2003 when ethnic African tribes began an armed campaign against the Khartoum government.
The government is accused of supporting militias known as the Janjawid who have been blamed for widespread atrocities.