BEIRUT—Lebanon’s parliament appointed billionaire businessman Najib Mikati as prime minister, choosing the candidate backed by Hezbollah and confirming the movement as the country’s most powerful military and political force.

The vote spurred occasionally violent protests by Sunni youths angry at the ouster of pro-Western Prime Minister Saad Hariri, raising fears that broader clashes could erupt along sectarian divisions in the country, which has long been a battleground for international rivalries.

In less than two weeks, Hezbollah’s leader Seyed Hassan Nasrallah has used local political alliances and the backing of Iran and Syria to topple Mr. Hariri, and install his candidate of choice to lead the country.

Mr. Nasrallah didn’t have to deploy his feared militia on the streets of Beirut in order to effect the change of power, as he has done in the past to settle disputes with the government.

Hezbollah’s military branch, supported by Iran’s Revolutionary Guard Corps, is considered better-armed and trained then the Lebanese army, and is viewed by many Arabs as the one military group in the region, other than Iran, capable of fighting Israel.

Hezbollah’s rise secures a stronger voice for the interests of Tehran and Damascus in Lebanon’s government, at the expense of reduced U.S. influence.

Hezbollah now faces a balancing act, aiming to exert greater control over Lebanese politics but at the same time avoiding overplaying its hand.

Israel has said it wouldn’t tolerate a government led by Hezbollah in Lebanon. The rise of Hezbollah is also likely to affect U.S. support for Lebanon. Secretary of State Hillary Clinton said Tuesday that “a Hezbollah-controlled government would clearly have an impact on our bilateral relationship with Lebanon.”

Hezbollah’s maneuvering may serve as a lesson for the region’s other radical groups—such as Hamas in the Gaza Strip and the followers of Moqtada al Sadr in Iraq—who often look to Mr. Nasrallah for inspiration in how to combine force with politics in order to extend their power.

“It’s a big dramatic change and a clear setback if you are talking about Western democratic ways we had tried to gain in the past few years,” said Paul Salem, the director of the Middle East Carnegie Endowment for International Peace.

In a televised speech Tuesday, Mr. Nasrallah said his party didn’t seek to rule Lebanon alone. The extent of the Shiite party’s role in government is ultimately limited by the country’s power-sharing system, which stipulates that the prime minister must be a Sunni, the president a Christian, and the house speaker a Shiite.

Mr. Mikati, 55 years old, is a parliamentarian and former prime minister widely seen here as a moderate centrist known for philanthropy. Many Sunnis said they didn’t object to him as a leader, but were angry that he was brought to power by Hezbollah.

In his victory speech on Tuesday, Mr. Mikati said that he hopes to bring stability and unity to his deeply divided nation and that he viewed himself as a consensus candidate not affiliated to the opposition.

Mr. Mikati’s immediate challenge is to negotiate with the different parties and form a new government. Mr. Hariri’s bloc has said it won’t participate in a new cabinet led by Mr. Mikati, a scenario that Mr. Mikati’s advisers say will likely lead him to name a cabinet of technocrats rather than of ministers from the leading political parties.

“My hand is extended to all Lebanese, Muslims and Christians, to build, not to destroy, to talk and not quarrel,” Mr. Mikati said in his speech.

But the developments risk alienating Sunnis and could tip the tenuous sectarian balance in the country, Jeffrey Feltman, assistant secretary for Near Eastern Affairs, said Tuesday.

In Mr. Mikati’s home city of Tripoli, young Sunni protesters waved sticks, burned tires and tore up pictures of the incoming prime minister.

The army guarded government buildings with tanks and military vehicles, and large groups of soldiers were deployed at most of the capital’s intersection.

By midday, the protests grew violent when a satellite truck belonging to the Arabic news channel al-Jazeera, seen here as pro-Hezbollah, was set on fire in Tripoli and gunshots were exchanged between the army and rioters.

The first priority of Mr. Mikati’s new government will likely be fulfilling the wishes of Hezbollah and its backers to cut Lebanon’s ties to the U.N.-backed international tribunal investigating the 2005 assassination of former Prime Minister Rafik Hariri, the father of Saad Hariri.

Sealed indictments issued last week are expected to accuse Hezbollah of a role in the car bombing.

Mr. Nasrallah and leaders in Iran and Syria have denounced the accusations. Hezbollah and Syria want the Lebanese government to cut ties with the tribunal, claiming it is influenced by Israel and the U.S.

In his address Tuesday, the Hezbollah leader had strong words for his opponents. “You have been plotting against us since 2005 after you made commitments to Washington. You asked for the war with Israel [in July 2006] and today comes the tribunal project to get rid of the resistance, but you will fail,” Mr. Nasrallah said.

Write to Farnaz Fassihi at farnaz.fassihi@wsj.com

Corrections & Amplifications:
Lebanon’s power-sharing system stipulates that president must be a Christian and the house speaker must be a Shiite. An earlier version of this article incorrectly said the president must be a Shiite, and the house speaker a Christian.