Prime Minister Rafiq al-Hariri resigned on Wednesday and declined to head the new government after sharp political differences with Syrian-backed Lahud.
Karami, a close ally of Syria, emerged as clear favourite after many MPs named him as their choice in consultations with Lahud.
The parliamentary consultations are compulsory for the president to name the new premier.
Presidential palace sources said the prime minister would be named later on Thursday.
About 22 opposition MPs said they would boycott the consultations, saying the names of the new prime minister and his cabinet had already been decided.
Al-Hariri's bloc in the 128-member parliament refused to name a candidate.
Karami, a 70-year-old member of parliament from the northern city of Tripoli, had been prime minister between December 1990 and May 1992.
He resigned after angry demonstrations in Beirut protesting the collapse of the Lebanese pound at the time.
Al-Hariri had been prime minister
for most of the last 12 years
Karami entered the political scene after his brother Rashid Karami was assassinated while serving as prime minister in 1987.
Once named prime minister, he would hold parliamentary consultations over the make-up of his cabinet before declaring the new government, a process that should be completed in a few days.
The government change comes as the United Nations and Washington heap pressure on Syria to relinquish its grip on Lebanon.
Lahud's term was extended last month under pressure from Damascus, drawing a UN Security Council resolution condemning foreign interference in Lebanon and demanding the withdrawal of foreign troops.
The US said it was concerned Syria would try to impose its will on the formation of a new government.
Damascus has had the last word politically in its smaller neighbour since the end of the 1975-1990 civil war, when it flooded Lebanon with troops.
Syria recently redeployed some
of its 16,000 troops in Lebanon
Lebanese officials have said Syria told them it would not intervene in the formation of the new cabinet - a move some commentators said gave the upper hand to Lahud in his rift with al-Hariri.
The extension of Lahud's term and international pressure over Syria's long shadow in Lebanon had paralysed the government, grappling with a debt of nearly $33 billion.
The new cabinet is to last only until May parliamentary elections in which al-Hariri could hope for a showing that ensures a strong role in the government or opposition.