Hezbollah, while not making any official statement yet, had privately conceded defeat, our correspondent said.
Ziad Baroud, the interior minister, said he would begin announcing official results within a few hours, but already March 14 supporters were celebrating in the streets.
Saying "the only winner is democracy and Lebanon", al-Hariri called on supporters of the rival camps to refrain from any provocation.
Security sources said one person was wounded by gunfire in the northern city of Tripoli and there were brawls between rival supporters elsewhere, but no reports of serious fighting.
Preliminary figures showed a turnout of more than 54 per cent, exceeding the 45 per cent total recorded in the 2005 election.
The figure is high for Lebanon, where hundreds of thousands of the 3.26 million eligible voters live abroad.
Long queues had formed outside polling stations during the day, with some people complaining that they had to wait for up to three hours to cast their ballots.