The vote on the resolution to send the observers came as activists reported 20 deaths in the country, nine of them in the restive city of Homs, where videos posted on the Internet showed government forces had renewed shelling, the Los Angeles Times reported.
A larger team of perhaps as many as 250 observers is to be sent to Syria later to monitor the cease-fire brokered by the U.N. and the Arab League.
The resolution is the first approved by the U.N. Security Council since the protests in Syria began in March 2011, and the United Nations estimates at least 9,000 people have died in violence in the country since then.
Russia had previously blocked the council's Syria resolutions but Russian Ambassador Vitaly Churkin said the country was satisfied with the language of the resolution requiring a halt to fighting, CNN reported.
"There have been too many casualties, too much suffering to befall the Syrian people," Churkin said.
He said the country has reached an "extremely critical juncture" and unrest there could affect regional peace and stability.
U.S. Ambassador Susan Rice welcomed approval of the resolution but said the United States was "under no illusions" about its immediate effect and continuing violence is "raising renewed doubts about the sincerity" of Syrian authorities to end hostilities.
She said the renewed shelling of Homs "absolutely" violates the cease-fire.
Violence also erupted in the northern city of Aleppo, where five people were killed, three of them when forces with the regime of President Bashar Assad opened fire on mourners at a funeral, CNN reported.
Syrian state TV reported the security forces had clashed with what it called armed terrorist groups -- the government blames "armed terrorists" for violence in the country -- and the state-run news agency SANA said two law enforcement officers were killed and an army colonel kidnapped in separate attacks by armed terrorists.
2014: The Year in Music [PHOTOS]