The 192-member assembly is expected to approve membership on Thursday. Independence from Sudan was gained Saturday, following a January referendum and decades of conflict.
A flag-raising ceremony was scheduled to take place almost immediately after approval by the General Assembly.
"The council notes with great satisfaction the Republic of South Sudan's solemn commitment to uphold the purposes and principles of the Charter of the United Nations and to fulfill all the obligations contained therein," said a Presidential Statement read out by Guido Westerwelle, foreign minister of Germany, this month's president of the 15-member council.
"We look forward to the Republic of South Sudan joining us as a member of the United Nations and to working closely with its representatives," the brief statement concluded.
The resolution said the application was "examined" and that the panel of 15 "Recommends to the General Assembly that the Republic of South Sudan be admitted to membership in the United Nations."
"On the day of its birth, South Sudan ranks at the bottom of almost all human development indicators," said UN Secretary- General Ban Ki-moon who attended the independence ceremony and celebrations Saturday in Juba, capital of the new state. "Like any newborn, South Sudan needs help."
"Our responsibilities are enormous and the role of the UN is vital, but it is complicated," he continued.
A peacekeeping mission is being established for South Sudan while Ethiopian peacekeepers have beeb deployed in the contested north-south border town of Abyei.
"The situation in Southern Kordofan is deeply troubling," Ban added.
The secretary-general said resolving the tensions was " absolutely vital" because, "A viable South will need a viable North -- and vice versa. Together, South and North must face their common future as partners, not rivals."
Vice President of South Sudan Riek Machar Teny-Dhurgon agreed.
He told reporters after the council meeting, "As the new baby to the community we have challenges."
But Teny-Dhurgon expressed confidence they would be resolved.