The agreement that paved the way for his election, reached in Doha on Wednesday, ended some of the worst violence since the country's 1975-1990 civil war.
An 18-month stalemate between the Christian, Sunni Muslim and Druze governing coalition and the pro-Syrian opposition - led by the Shia Hezbollah political and militant group - had brought the country to crisis point.
The army chief, who was standing unopposed, is widely seen as a trusted figure who has managed to maintain the army's neutrality among Lebanon's complex mix of factions.
Applause broke out in the chamber as speaker Nabih Berri announced that Gen Suleiman had won 118 votes out of 127.
Trumpets played and supporters waved flags in the streets, while celebratory gunfire resounded around the capital, Beirut.
"Let us unite... and work towards a solid reconciliation," Gen Suleiman said after he was sworn in. "We have paid dearly for our national unity. Let us preserve it hand-in-hand."
In a speech seen as reaching out to both sides of Lebanon's political divide, Gen Suleiman said the country should co-operate with UN efforts to try suspects in the killing of former Lebanese Prime Minister Rafik Hariri.
Many Lebanese are relieved to finally have a president
But he also called for "brotherly ties" with Syria and a "national strategic stance" so that Lebanon could "benefit from the lessons of the resistance [Hezbollah] to serve the nation".
The outgoing Western-backed governing coalition had pushed for the UN tribunal and blamed Syria for Hariri's death, while correspondents say the role of Hezbollah as an armed movement is one of the most sensitive facing the new president.
The BBC's Jim Muir in Beirut says the first hurdle facing the new president is to form a national unity government, as agreed in last week's deal after days of talks in Qatar.
Under the agreement, the opposition gained the power of veto in a new cabinet of national unity - over which it had walked out of the previous cabinet 18 months ago.
While the make-up of the government has been agreed, our correspondent says there will be much haggling over who gets which portfolio.
Western-backed ruling majority to get 16 cabinet seats and choose prime minister
Syrian-backed opposition to get 11 cabinet seats and veto power
Three cabinet seats to be nominated by president
The use of weapons in internal conflicts is to be banned
Opposition protest camps in central Beirut are to be removed
New law to divide country into smaller electoral districts
Our correspondent says it was a huge relief for many Lebanese to find themselves with a new president at last, after 19 failed attempts to elect a head of state.
But, he adds, Gen Suleiman comes into office with his wings somewhat clipped, after his army was humiliated by having to stand by while Hezbollah burned newspaper offices and nearly stirred up civil war in the violence which broke out two weeks ago.
At least 65 people died in clashes as Hezbollah fighters seized control of sections of Beirut in response to government attempts to outlaw the group's private telephone network and reassign Beirut airport's security chief, who is close to the opposition.
US President George W Bush welcomed Gen Suleiman's election and said he looked forward to an "era of political reconciliation".
"I am confident that Lebanon has chosen a leader committed to protecting its sovereignty, extending the government's authority over all of Lebanon, and upholding Lebanon's international obligations under UN Security Council Resolutions," Mr Bush said in statement.
Fireworks and celebratory gunfire rang out across Beirut
Among 200 guests at the parliamentary vote were the Emir of Qatar, who helped mediate the Doha deal, as well as a US congressional delegation and the foreign ministers of Iran, Syria and Saudi Arabia.
Our correspondent says these outside powers have all been involved in the proxy struggle in Lebanon, but now seem to be coming together to give their blessing to the agreement.
For months, Gen Suleiman had been accepted by all sides as the only candidate to succeed outgoing pro-Syrian President Emile Lahoud, but disagreements had repeatedly prevented a parliamentary vote to appoint him.
Our correspondent says his election does not mean the military is taking over - it is more a case of feuding politicians being unable to agree on a Maronite Christian, which the president has to be, who is acceptable all round.
Under the constitution, outgoing Prime Minister Fouad Siniora is expected to head a caretaker government until a new prime minister is appointed.
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