"This government is either an opportunity to renew our trust in the state and its institution or a new stage to repeat our failure in achieving consensus," Hariri told a news conference after meeting Sleiman at the presidential palace.
"We look forward to a government that works for Lebanon."
'Right to resist'
Shia Muslim Hezbollah, which fought a two-month war with Israeli forces in the summer of 2006, will get two ministers in the cabinet under the deal.
Rula Amin, Al Jazeera's correspondent in Beirut, said: "Many people will say that the number of ministers Hezbollah will get in the government is irrelevant in terms of what they have got politically.
"We have to remember that in the previous unity government they had only one minister.
"In this cabinet they will have two, but more importantly they will have a policy statement, issued by the government, which will indirectly endorse, as they say, their right to resist and to have weapons."
The group, which is designated as a terrorist organisation by Washington, is the only Lebanese faction that has openly refused to disarm since the end of the 1975-90 civil war.
It says its fighters need to keep their weapons in order to protect Lebanon from a possible attack by neighbouring Israel.
Lebanon has been without a functioning government since Hariri - who is backed by the US and Saudi Arabia - led his coalition, which many describe as anti-Syrian, to victory in the parliamentary elections.
A warming of ties between Syria and Saudi Arabia in recent weeks helped ease the rift in Beirut and led eventually to the breakthrough.
The rival factions had agreed in July on the broad division of seats in the new cabinet.
But Hariri, son of Rafiq al-Hariri, the assassinated former prime minister, had struggled to reach agreement with opposition politicians on the details.
At the heart of the disputes were the demands of Christian leader Michel Aoun, an ally of Hezbollah. Aoun's Free Patriotic Movement holds more seats in parliament than any other Christian party.
Amin reported that the list provided by Hariri was "a true national unity government".
"All the Lebanese factions are represented. But the winner of all the Lebanese political parties is going to be considered to be Aoun, the Christian Maronite leader, he is going to get five ministers," she said.
"It was his demands to get the ministries he was demanding that delayed the government for over a month ... he got all that he wanted."
France, Lebanon's former colonial ruler, welcomed the formation of the Lebanese government and pledged support for Hariri.
"The formation of a new government was necessary to resolve the conflict that Lebanon was facing, to assure the security and stability of the country," Bernard Kouchner, the French foreign minister, said.
He urged the new government to push through economic measures demanded by donors and implement UN Resolution 1701 that ended
the 2006 war.