After nearly three months of protracted political haggling, the vote took place on Wednesday, a senior member of the ruling alliance said.
Quoting al-Jafari, Aljazeera said a list containing the names of those who will assume ministerial portfolios, has been submitted to the presidential council.
The announcement came shortly after armed men shot and killed a member of Iraq's parliament outside her home in eastern Baghdad.
Iraqi police identified the victim as Lamia Abid Khadawi, a member of caretaker Prime Minister Iyad Allawi's political party.
Khadawi is thought to be the first person in the 275-member National Assembly to be killed.
Officials said late on Tuesday that al-Jafari had presented his government lineup to President Jalal Talabani.
But he did not make the names public because of last-minute disagreements over some appointments, particularly for the oil and interior ministries, an aide said.
PM-designate al-Jafari makes
the announcement in Baghdad
There was no immediate word on whether all differences had been resolved on Wednesday.
Iraqi media said one possible scenario envisaged the United Iraqi Alliance (UIA) getting 17 cabinet posts. The Kurds would get nine portfolios, including the Foreign Ministry, while Sunni Arabs would get seven portfolios, including the Defence Ministry.
The Christian and Turkmen minorities were expected to get one ministry each.
Iraqi media sources said Sadun al-Dulaymi, a Sunni, would be named defence minister.
In an effort to spread power among the nation's ethnic groups, al-Jafari would choose three deputy premiers: Roj Nuri Shaways, a Kurd, former Pentagon favourite Ahmad Chalabi and Sunni legislator Saad al-Lahabi.
Several ministers would remain at their posts, including Foreign Minister Hushiar Zibari, a Kurd, and Minister of Public Works Mustafa Barwari.
Iraqi media said Sami al-Majun would become minister of justice and Ali Abd al-Amir Allawi would be minister of finance.
Supporters of Allawi were not expected to participate in the new government after al-Jafari rejected their terms.
UIA member of parliament Ali al-Dabbagh denied that names recommended by the Sunnis for cabinet berths had been changed.
"On the contrary. We had a meeting with the Sunnis. Today we met with Salih al-Matallaq and with the members of the national dialogue committee. They introduced their list and their proposals were accepted. We are aware that the Sunnis are composed of more than one group. Accordingly, they proposed several name lists," he told Aljazeera.
He said al-Jafari had the discretion to select names from different lists. "But finally, the recommendations of the national dialogue committee were respected and most of Sunni-recommended names were approved".
In Wednesday's other violent incidents, an Iraqi general was seriously wounded in a drive-by shooting while leaving his Baghdad home, an Interior Ministry official said.
Hushiar Zibari is tipped to retain
his foreign minister's post
Two of the general's bodyguards were killed and a passing civilian was injured.
General Jihad Luaibi, a police anti-corruption inspector-general, was transferred to a US-run hospital after armed men in two cars opened fire outside his home in a western district of the capital.
Aljazeera learned that armed men also attacked Interior Ministry undersecretary Major-General Hikmat Musa's home in al-Ghazaliya district in west Baghdad on Wednesday.
The attack, involving grenades and machine guns, left a Musa bodyguard wounded.
In Samarra, an Iraqi policeman was killed and three others were wounded when an explosive device blew up, Aljazeera added.
And in Basra, an Iraqi policemen was killed when armed men attacked a police patrol with machine guns.