The UN resolution has been condemned by Hezbollah, Lebanon's main Shia political faction, as an illegal "interference in [Lebanon's] internal affairs".
Fouad Siniora, Lebanon's prime minister and a key member of the political majority, says that the Hezbollah-led opposition is being manipulated by allies in Damascus to block the formation of the court.
Al-Hariri, an opponent of Syria's domination of Lebanon, was killed with 22 others in a bomb blast in Beirut in February 2005.
His killing led to widespread anti-Syrian public demonstrations which eventually forced Syria's removal of its troops and security officers from Lebanon in April 2005.
The trial and appeals chambers of the new court will consist of both Lebanese and international judges, with foreign participants to be named by Ban Ki-moon, UN secretary-general.
The international court, which will be held in an as yet un-named neutral location, will not be up and running for several months, diplomats and UN officials say.
Nine suspects, including Lebanon's senior pro-Syrian security leaders, have been under arrest for about two years over the killing and may stand trial before the court.
Walid Muallem, Syria's foreign minister, said last week that Damascus would not co-operate with the tribunal.