The resolution will set June 10 as the date for implementation of an agreement between the UN and Beirut to establish the court.
In any case, the tribunal is not likely to be up and running until several months after the accord enters into force.
Marwan Hamada, Lebanese telecommunications minister, said the resolution was a historic moment.
Speaking to Al Jazeera on Wednesday, 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'.
"It is high time, after we get this resolution, to go back to national dialogue in Lebanon"
Marwan Hamada, Lebanese Telecommunications Minister
"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."
An initial UN investigation implicated top-level Syrian figures and their Lebanese accomplices in the assassination of al-Hariri, who served as prime minister five times and was killed by a huge roadside blast in Beirut on February 14, 2005.
But the 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.
Al-Assad earlier this month said he ruled out any co-operation with the court if it threatens his country's sovereignty.
Both sides of the political divide have said the latest troubles in Lebanon, which have seen close to 80 people killed in the worst fighting since the 1975-1990 civil war, were stirred up because of the impending UN decision.
|Rafiq al-Hariri was killed by a huge roadside|
bomb in Beirut on February 14, 2005 [AP]
Al-Hariri's son Saad, the head of the parliamentary majority, accused Syria of planning to create a "fifth column ... to try to provoke people and show that the creation of the tribunal would lead to grave problems in Lebanon".
Appealing for his supporters to remain calm, Hariri said: "The goal of the court is not to avenge a single person but to protect Lebanon from the terrorist campaign against it over the past three decades."
But the 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."