A total of 69 deputies from the 128-member chamber on Wednesday chose Karami, a favourite of Syria, in consultations with President Emile Lahud, the sources said in Beirut.
The president, also close to Damascus, was now bound to appoint Karami, who resigned last week under popular and opposition pressure, as prime minister-designate.
Opposition MPs did not nominate anyone to lead the government, handing Lahud a list of their demands instead.
They included calls for the resignation of the country's security chiefs and a demand for the authorities to reveal who was behind the 14 February assassination of former prime minister Rafiq al-Hariri.
A top diplomat said Syrian troops
will be out of Lebanon before May
Karami will have the task of forming a government of national unity, bringing in a number of opposition figures, the sources said. The previous government, which quit last week, comprised only pro-Syrian ministers.
Meanwhile, Syria's ambassador to the United States said his country's troops would be out of Lebanon by May, when legislative elections are to be held.
"They are actually being withdrawn today," Imad Mustafa told CNN television on Tuesday. "We will do this as soon as possible, even long before May."
The comment followed a fresh call by US President George Bush for Syria's military and intelligence forces to be out of Lebanon before the elections.
Lebanon's caretaker Defence Minister Abd al-Rahim Murad said the redeployment of 6000 Syrian troops towards the eastern Bekaa Valley had begun on Tuesday and would take a week to 10 days.
"They (Syrian troops) are actually being withdrawn today"
Syria's ambassador to the US
The withdrawal would also cover Syrian intelligence personnel, including their headquarters in Beirut, a senior Lebanese military official said.
Syrian President Bashar al-Asad on Monday pledged to pull back his country's remaining 14,000 troops in Lebanon towards the Bekaa, where most of the troops are already based, by the end of March.
But he stopped short of announcing a full withdrawal.
Under the 1989 Taif Accord that ended the 1975-1990 civil war in Lebanon, the Syrian and Lebanese governments are to decide the strength of the Syrian force remaining in the Bekaa and when they would be withdrawn completely.