Lebanon's president has appointed Najib Mikati, who is backed by the Shia Islamist group Hezbollah and its allies, as prime minister-designate.
The move came despite demonstrations by thousands of supporters of outgoing Prime Minister Saad Hariri in the city of Tripoli as part of a "day of rage".
Smaller protests were also reported in the capital, Beirut, and elsewhere. Mr Hariri has condemned acts of violence.
Analysts say many Sunnis are alarmed by Hezbollah's growing political power.
They accuse the Iran-backed group of staging a "coup", because it brought down the Western-backed government earlier this month.
On Tuesday, it became clear that Hezbollah had gained enough support from parliamentary deputies to allow Mr Mikati, a billionaire Sunni businessman, to form the next government.
The US has said it would have "great concerns about a government within which Hezbollah plays a leading role".
Lebanon's national unity cabinet collapsed on 12 January after a row over a UN tribunal investigating the 2005 murder of Rafik Hariri, the father of Western-backed caretaker Prime Minister Saad Hariri.
Mr Hariri had refused to renounce the UN inquiry that reports say will implicate senior Hezbollah figures in his father's murder. Hezbollah says the investigation is politically motivated.'Moderate'
During consultations with President Michel Suleiman on Tuesday, 68 members of parliament expressed support for Mr Mikati, who served briefly as premier in 2005 - as opposed to 60 who backed Mr Hariri.
It was the decision of Druze leader Walid Jumblatt and six members of his Progressive Socialist Party to switch their allegiance from Mr Hariri that swung the vote, but Hezbollah's support was central to his nomination.
After his appointment was confirmed, Mr Mikati said he hoped the new government would serve all of Lebanon, and protect its unity and sovereignty.
"This does not signal the victory of one camp over another," he told reporters. "This is the victory of consensus over difference."
He said nothing justified the refusal of any political party to participate in the next government, adding: "My hand is extended to all Lebanese."
"I look forward to seeing the new government act as one that faces - with a sense of collective national responsibility - all the challenges awaiting us and one that lives up to aspirations and hopes of the Lebanese people."
Under Lebanon's power-sharing system, the post of prime minister is reserved for a Sunni, while the president must be a Maronite Christian and the speaker of parliament a Shia.
Earlier, Mr Mikati told the BBC that although he needed the votes of Hezbollah, he remained independent of the movement.
"I am not at all related to Hezbollah by any means," he told the BBC.
"I am a moderate guy, I am a moderate politician. I am always at equal distance from everybody," he added.
"My objective is the interest of Lebanon and the interest of the nation, the international security of Lebanon and especially to have a good relationship with the international community."Streets blocked
Earlier, Mr Hariri went on television to appeal for calm as thousands of his supporters staged street protests against the appointment.
TV pictures from the predominantly Sunni city of Tripoli - Mr Mikati's hometown - on Tuesday morning showed an angry crowd waving banners and holding aloft pictures of Mr Hariri and his father, and tearing down posters of the new prime minister-designate.
Medical sources said 20 people were treated for injuries, and protesters attacked and then set alight a satellite truck used by al-Jazeera TV.
Schools and shops in the Tripoli area had closed down in anticipation of the protests on what was dubbed a "day of rage", following similar protests on Monday.
Protests were also reported in Beirut, where crowds overturned rubbish bins and blocked streets, and the mainly Sunni southern coastal city of Sidon.
In his speech, Mr Hariri thanked "every free citizen" who had "denounced the attempts of hegemony over our national citizens".
"But it is also my duty to express my total rejection of all forms of rioting and acts of law-breakers who have accompanied these demonstrations," he said.
"You are angry but you are responsible people," he added. "This anger should not lead us to what disagrees with our values... our belief that democracy is our refuge."
Mr Hariri, who has refused to join any Hezbollah-led administration, also said he deeply regretted the attack on al-Jazeera's vehicle.
The protesters' anger is fuelled by the fact that they appear to have been outmanoeuvred by Hezbollah, says the BBC's Kevin Connolly in Beirut.
Although this crisis was triggered by allegations that Hezbollah figures were involved in Rafik Hariri's murder, it appears to be resulting in greater power in the group's hands, our correspondent says.
The question now, he adds, is what kind of prime minister Mr Mikati will be, and what kind of government he will head.
It is not known if Mr Mikati will end the government's co-operation with the Special Tribunal for Lebanon (STL), as demanded by Hezbollah. On Sunday, he said any dispute could "be solved only through dialogue".