While not expecting an immediate breakthrough, UN-mediator Staffan de Mistura has said this could be the first "real negotiation".
Staffan de Mistura's statement came a day after the opposition named its unified delegation that includes internal and external groups to the Geneva talks which will start Tuesday.
"Hariri was selected as the head of the delegation today", opposition member Jamal Suleiman said on Friday.
This follows Vladimir Putin's meeting with Bashar al-Assad in Sochi, agreeing on the need for a new constitution and new elections.
US President Donald Trump said following a phone conversation with French leader Emmanuel Macron that the two agreed the Geneva talks were the "only legitimate forum for achieving a political solution in Syria". Putin has also proposed a congress between the warring sides.
The regime's bombardment of Eastern Ghouta, one of the last remaining opposition strongholds, has killed more than 100 people in the past two weeks, according to the Observatory. It comes after three days of intense negotiations between various opposition groups in Riyadh.
Russian Federation supports Assad's government and provides air support for government forces.
Following a closed-door session, Italian Ambassador Sebastiano Cardi, who holds the council presidency, told reporters that there was strong backing for the UN-led negotiations.
"I will continue to view this proposal and all other initiatives through the same prism: does it contribute to effective UN-led intra-Syrian negotiations in Geneva to implement resolution 2254", he said.
"The meeting will start tomorrow and we really hope that all parties, including the Syrian government, will be present", said Cardi.
Syria's disparate opposition has been under heavy pressure to unify their ranks and row back on some of their more radical demands after a series of battlefield victories that have given Mr Al Assad's regime the upper hand.
He said he is invited to participate in a preparatory meeting on Tuesday that France organized to bring together representatives of the five permanent members of the Security Council - China, France, Russia, United Kingdom and the United States - in Geneva.
Syria's reconstruction is expected to cost $250 billion, said the United Nations envoy.
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