The plan, put forward by UN special envoy James Baker, would make the territory a semi-autonomous part of Morocco for four to five years.
A referendum would then let residents choose between independence, continued semi-autonomy or integration with Morocco.
US ambassador John Negroponte said the resolution "represents a considered recommendation of the council to the parties and neighbouring states, but does not constitute an imposition."
"The peace plan is a fair and balanced compromise giving each party some but not all of what it wants," he told council members.
Last minute diplomacy
The language of the resolution was softened at the last minute to allow both sides to claim victory.
"The peace plan is a fair and balanced compromise giving each party some but not all of what it wants" -- John Negroponte
France led the battle against the US text, arguing it was not favourable enough to Morocco, which seized control of the sparsely populated desert territory nearly three decades ago.
The Algerian-backed Polisario Front independence movement have long resisted any resolution of the impasse other than a referendum on independence.
It endorsed the Baker plan earlier this month, only to find Morocco then bridle.
The Polisario said the resolution showed the Baker plan must now be accepted by all sides, while Morocco said the text had merely opened the way to further negotiations.
The Western Sahara conflict has proved one of the most intractable disputes in recent north African history.
The territory is rich in phosphates and may also have offshore oil deposits, making it a prized possession for its rulers.