The Lebanese opposition, led by the Shia group Hezbollah, has vowed it will never accept the tribunal and blocked government efforts to win parliament's endorsement for the project.
Ali Hassan Khalil, an opposition MP, said: "Do not expect that we will recognise this tribunal, directly or indirectly."
"It is high time, after we get this resolution, to go back to national dialogue in Lebanon"
Marwan Hamada, Lebanese Telecommunications Minister
Michel Aoun, a Christian opposition leader, also deplored that no suspects had been identified despite moves to fast-track the international court.
"What is most important for the tribunal is to have people who are accused. Where are the accused?" he said in an interview to France Inter radio before the vote.
Wednesday's resolution gives the Lebanese parliament a last chance to establish the tribunal itself. If it doesn't act by June 10, the UN-Lebanon agreement will automatically "enter into force".
However, the tribunal is not likely to be up and running until several months after the accord enters into force.
The Security Council vote was 10-0 with five abstentions - Russia, China, South Africa, Indonesia and Qatar.
Fouad Siniora, the Lebanese prime minister, asked the council earlier this month to establish the tribunal.
He cited the refusal of Nabih Berri, the opposition-aligned parliament speaker, to convene a session to ratify the statutes to create the tribunal.
Rafiq al-Hariri and 22 others were killed by a massive truck bombing in Beirut on February 14, 2005, and the Security Council authorised a commission to investigate the assassinations.
|Hariri supporters in Lebanon cheer the news of|
the Security Council vote [AFP]
The UN inquiry panel implicated senior Syrian figures and their Lebanese accomplices in the assassination.
But the Syrian government of Bashar al-Assad, who won another seven-year term in a weekend referendum in which he was the only candidate, has denied any involvement.
He earlier this month said he ruled out any co-operation with the court if it threatens his country's sovereignty.
Reacting to Wednesday's vote, Syria said in a statement: "Setting up the court under Chapter Seven violates the sovereignty of Lebanon and could cause the situation there to become worse. There has been no change in the Syrian position on the court."
Despite the calls for unity, the Lebanese government appeared fearful that celebrations could turn violent between pro-government and opposition factions.
The interior ministry banned the public from firing guns in the air, releasing fireworks and using motorcycles from 8pm (1700 GMT) on Wednesday to 5am (0200 GMT) on Thursday.
Supporters began celebrating in al-Hariri's hometown in the southern city of Sidon more than six hours before the Security Council met in New York.
Carrying Lebanese flags and pictures of Rafiq al-Hariri, supporters set up what they called "love checkpoints" in Sidon's main roads and intersections handing out sweets and flowers to motorists.
Marwan Hamada, Lebanese telecommunications minister, said on Wednesday the resolution was a historic moment.
|Rafiq al-Hariri was killed by a huge roadside|
bomb in Beirut on February 14, 2005 [AP]
Speaking to Al Jazeera on the eve of the Security Council vote, he said: "We have to recall that the sovereignty of Lebanon has been hijacked for years and even recently by some of the opposition parties related to the Syrian regime.
"It is high time that an international resolution comes and contains the criminals and gives Lebanon an kind of 'legal umbrella'.
"We don't want military intervention or sanctions against anybody – but we need the sovereignty and independence of Lebanon to be respected.
"It is high time, after we get this resolution, to go back to national dialogue in Lebanon."
Source: Al Jazeera and agencies