Karami's appointment on Thursday came a day after Hariri resigned amid international criticism of the influence Syria wields over its tiny neighbour.
Presidential press secretary Rafiq Shlala said in a statement that "Mr Lahud had received Mr Karami and charged him with forming a new government".
Karami, 70, told reporters he would begin discussions on that task on Friday.
He said he considered his principal task to be one of opposing outside pressure on Lebanon and Syria and to pave the way for legislative elections in seven months.
"It is our duty to confront with spirit and an open heart during this delicate period external pressures on Lebanon and on Syria," Karami said after his meeting with Lahud, apparently in reference to moves by the international community to get Syria to reduce its influence on Lebanon.
Hariri resigned as prime minister
amid a worsening political crisis
"My government will last seven months, until legislative elections," he added, promising to arrange elections in such a way as to "allow the best popular representation".
The current crisis erupted on 3 September, when parliament approved a controversial Syrian-inspired constitutional amendment extending Lahud's mandate for another three years.
That move came only hours after the UN Security Council adopted a resolution calling for all foreign troops to be withdrawn from Lebanon and an end to outside interference in its affairs.
Syria has around 16,000 troops on the ground in Lebanon, the remains of a much larger force sent in during the 1975-1990 civil war.
"I will attempt to introduce reforms and stop the waste, but the problems are numerous and enormous ... . I have no illusions," Karami added.
Lebanon is facing a serious economic crisis with debts of around $35 billion as well as perceived widespread corruption.
A prominent Sunni Muslim figure in the northern city of Tripoli, Karami was premier from December 1990 until May 1992, when he was succeeded by first-timer Hariri after being forced out by nationwide protests over the economy.
Syria's 16,000-strong presence in
Lebanon is under critical scrutiny
Currently a member of parliament, he is a conservative politician with strong ties to Syria.
Under the complex arrangements of Lebanon's constitution, the prime minister is always selected from the Sunni community, while the president is always a Maronite Christian and the parliamentary speaker a Shia Muslim.
Karami was widely tipped to succeed Hariri, with the media predicting on Thursday that he would form a government of "confrontation", with the opposition and Western powers demanding Damascus pull its troops out of Lebanon.
The departure of Hariri, who is credited as the driving force behind Lebanon's reconstruction after the devastating civil war, has cast a large cloud over the country as it grapples with a deepening economic crisis.
Lahud, a longtime political rival of Hariri, held a constitutionally mandated series of meetings with MPs on Thursday before naming Karami.
But the meetings were widely believed to be no more than a formality, with several MPs already saying Karami would be picked.
An official tally released on Thursday evening said that 82 of 128 MPs supported Karami. The 16 members of Hariri's bloc declined to support anyone. Anti-Syrian Christian MPs and the 18-strong group of prominent Druze leader Walid Jumblatt refused to participate.
Jumblatt said on Wednesday that there was no point in doing so "because the make-up of the government has been decided in advance".
Following Hariri's announcement, US State Department spokesman Richard Boucher told Syria the selection of a new premier should be "a purely Lebanese process".
"The make-up of the government has been decided in advance"
The departure of Hariri, who has close ties to Western leaders and financial creditors including Saudi Arabia, has raised concerns over the precarious economic health of the country.
Meanwhile, US Secretary of State Colin Powell on Thursday voiced his dissatisfaction with Lahud's choice of PM saying it is further evidence of Syria's "inappropriate" role in Lebanon.
"When we see the personnel changes that have taken place with Mr Hariri stepping down and others coming into positions of power who are even more closely linked to Syria, [it] once again shows that Syria is playing an inappropriate role in political life and in the civic life of the Lebanese people," he said in an interview with Abu Dhabi television.
Powell: Syria should allow the
Lebanese people to decide
Powell did not mention Hariri's successor by name but made clear that Washington had concerns about the role Damascus may have played in the selection of Karami.
"Syria should allow the Lebanese people to decide how they will be governed, and they should remove their military forces from Lebanon after all these years," Powell said, according to a transcript of the interview released by the State Department.
"I hope the Syrians realise that we are now in a new age," he said. "Things are different and it is time for them to examine their strategic position on policies they have been following and adopt policies that are more relevant to the new world that we're in."