The resolution calls for further efforts to stop the spread of nuclear arms, to boost disarmament, and to lower the risk of "nuclear terrorism".
It was the first time US president had chaired a Security Council meeting.
The resolution comes amid growing concerns among world powers over Iran's nuclear ambitions.
The resolution adopted on Thursday reaffirms the council's commitment "to seek a safer world for all and to create the conditions for a world without nuclear weapons", the Associated Press reported.
It was also reported, the resolution also endorses a string of measures intended to strengthen the Non Proliferation Treaty (NPT), ahead of a major review conference next May.
Those measures focus on attempts to raising the costs of exiting the treaty, so that states cannot import nuclear technology as NPT signatories, build up a civil nuclear programme legally, and then walk out of the treaty and divert their programme to building weapons, all without breaking international law.
The resolution urges exporting countries to make sales of nuclear technology conditional on the customer nation agreeing to intrusive UN inspections, and requiring the return of the technology in the event of withdrawal from the NPT.
The relevant clauses are all non-binding representing the difficulty of finding consensus among the council members. France, in particular, had objected to strong language calling directly for the abolition of nuclear weapons. Mexico wanted more of the resolution to require action from the weapons states with less onus on the non-weapons states.
News agencies also report, President Obama is used the forum of the U.N. Security Council to press his efforts to slow the spread of nuclear weapons and reduce global stockpiles.
Diplomats have finished negotiating a Security Council resolution that affirms many of the steps Obama plans to pursue as part of his vision for an eventual "world without nuclear weapons." They include a new worldwide treaty halting production of weapons-grade uranium and plutonium and the strengthening of the global Non-Proliferation Treaty, which has controlled the spread of nuclear weapons for decades but now is in danger of fraying.