The resolution, sponsored by Great Britain and France, would authorize sending around 19,500 military personnel and 6,500 civilian police to the region.
More than 200,000 people have died in the past four years during fighting between rebels and militia forces in Darfur, and millions more have fled their homes.
"The situation in Darfur is the worst humanitarian disaster the world faces today," U.K. Prime Minister Gordon Brown told a U.N. audience Monday, at his first visit to the U.N. headquarters in New York as prime minister.
"We will work hard to deploy this force quickly," Brown said, according to the BBC. "But we must be clear: If any party blocks progress and the killings continue, I and others will redouble our efforts to impose further sanctions."
The resolution had been opposed by Sudan and by China, its ally on the Security Council. However, it was approved after council members removed some of its harsher language, including threats of sanctions and the right to seize and dispose of unauthorized arms, which will now be "monitored" instead, Reuters reported.
The resolution invokes Chapter 7 of the U.N. charter, which authorizes the use of force to protect both civilians and U.N. personnel.
The U.N. force, which will be called UNAMID -- the United Nations African Union Mission in Darfur -- will take over from the 7,000-member African Union force already in the area. However, infantry soldiers will still mainly be drawn from African countries, unless there are not enough African soldiers to fill the positions, according to Reuters. The United States plans to contribute financially and by transporting troops to the area.
The resolution sets a 30-day timeline for U.N. member-states to finalize their contributions to the force and for U.N. Secretary-General Ban Ki-moon to finalize its composition. It also sets an October deadline for establishing a headquarters in Darfur, and a Dec. 31 deadline for taking over from African Union forces. The estimated cost is more than $2 billion in the first year.