Romanian Foreign Minister Mihai Razvan Ungureanu, whose country currently holds the rotating presidency of the UN Security Council, announced the vote.
"The draft resolution received 15 votes in favor. The draft resolution has been unanimously adopted as Resolution 1636 from 2005," Ungureanu said.
At the urging of China and Russia, the five permanent and 10 nonpermanent Security Council members backed a weaker version of the original resolution.
The original text, which was was co-sponsored by the United States, Great Britain, and France, had threatened Syria with possible sanctions if it failed to cooperate.
The resolution that was approved today -- unlike the original draft -- does not mention sanctions. The text merely warns Syria of possible further action if continues to block the UN probe.
A report by a UN investigating commission has implicated top Syrian and Lebanese security officials in Hariri's killing in February.
Syria has strongly denied the charges.
(with news agencies/CNN)