The General Assembly is expected to approve the council recommendation June 28.
The tiny republic declared independence from Serbia on June 3 after its citizens voted for the split by a slim margin. The declaration marked the final breakup of what was once Yugoslavia, a process that began when the federation of six republics disintegrated in violence in the 1990s.
The Security Council adopted the resolution by consensus hours after Serbia and Montenegro established diplomatic ties.
"We look forward to the Republic of Montenegro joining us as a member of the United Nations and to working closely with its representatives," said Foreign Minister Per Stig Moeller of Denmark, whose country holds the Security Council presidency this month.
Once approved as a U.N. member, Montenegro will see its flag raised alongside the other member states at a ceremony outside U.N. headquarters.
Montenegro was an independent kingdom in the late 19th and early 20th centuries, but it abandoned its statehood to join a new Serb-led Balkan union in 1918.
Montenegro, with 620,000 people, was the only republic to stay with Serbia, but it gradually edged toward independence during the autocratic rule of former Yugoslav President Slobodan Milosevic, who died earlier this year while on trial at the U.N. war crimes tribunal for his part in the bloody breakup of Yugoslavia.
Since the independence referendum, Montenegro has been recognized by the 25-nation European Union, the United States and scores of other countries. State Department spokesman Sean McCormack said last week the United States believes the possibility of eventual Montenegrin membership in NATO should remain open.
Serbia supported preserving the union with Montenegro and initially disputed the results of Montenegro's referendum, fueling fears of tension between the two nations. Serbia opposed previous declarations of independence by Slovenia, Croatia and Bosnia, triggering nearly a decade of wars.
But the establishment of diplomatic relations Thursday between Serbia and Montenegro was seen as a hopeful start to building good neighborly relations.
Since the alliance broke up at Montenegro's initiative, Serbia automatically inherited Serbia-Montenegro's seat in the United Nations.