The document describes the deliberate use of rape as a tactic in war and a threat to international security.
UN Secretary General Ban Ki-moon said violence against women had reached "unspeakable proportions" in some societies recovering from conflict.
The UN is also setting up an inquiry to report next June on how widespread the practice is and how to tackle it.
Human rights groups hailed the resolution as historic.
The BBC's Laura Trevelyan said China, Russia, Indonesia and Vietnam had all expressed reservations during the negotiations, asking whether rape was really a matter for the security council.
But the US-sponsored resolution was adopted unanimously by the 15-member council.
It's a very effective weapon, because the communities are totally destroyed
Maj Gen Patrick Cammaert
Former UN peacekeeper
It described sexual violence as "a tactic of war to humiliate, dominate, instil fear in, disperse and/or forcibly relocate civilian members of a community or ethnic group".
The document said that the violence "can significantly exacerbate situations of armed conflict and may impede the restoration of international peace and security".
During the debate in the council, Mr Ban said: "Responding to this silent war against women and girls requires leadership at the national level."
"National authorities need to take the initiative to build comprehensive strategies while the UN needs to help build capacity and support national authorities and civil societies," he added.
US Secretary of State Condoleezza Rice said the world now recognised that sexual violence profoundly affected not only the health and safety of women, but the economic and social stability of their nations.
Other speakers identified the former Yugoslavia, Sudan's Darfur region, the Democratic Republic of Congo, Rwanda and Liberia as regions where deliberate sexual violence had occurred on a mass scale.
The former commander of the UN peacekeeping force in eastern Congo, Maj Gen Patrick Cammaert, told the BBC he had personally witnessed its impact.
"It's a very effective weapon, because the communities are totally destroyed," he said.
"You destroy communities. You punish the men, and you punish the women, doing it in front of the men."
In the Democratic Republic of Congo alone, some 40 women are raped every day, our correspondent says.
Sometimes women are even raped by peacekeepers who are supposed to be protecting them, she adds.
The question is whether those in conflict zones who use rape in war will be at all deterred by the new measures, she says.