Al-Jafari,currently the vice president of Iraq in the interim government, is a religious Shia and head of the Islamist Dawa Party.
He had faced competition from inside the alliance from former exile Ahmad Chalabi, once favoured by the Pentagon, but Chalabi withdrew and the alliance's 140 members unanimously approved al-Jafari, alliance sources said.
Some of Chalabi's aides, including Qaisar Witwit, have suggested he may be offered the post of deputy prime minister in charge of economic and security affairs.
When asked about the reported deal, Chalabi said simply: "We will see."
"The security situation is the first matter we will address"
Al-Jafari still faces a challenge from incumbent interim Prime Minister Iyad Allawi, but Allawi's list won only 14% of the vote in last month's election.
The Shia alliance won 48% and has insisted it must have the prime minister's job, and looks certain to get it.
Al-Jaafari has said dealing with anti-US fighters and re-establishing security would be his main priorities if he became prime minister.
"The security situation is the first matter we will address," he said.
The Shia parties, which failed to win an outright majority, have been in intense negotiations with each other over who would be chosen as prime minister.
Last week, talks were suspended for the Shia holy festival of Ashura, commemorating the martyrdom of the Prophet Muhammed's grandson al-Husain.
Ties to Iran
But al-Jafari's ties with Iran and presumed support for a more Islamic state have sparked concern.
Al-Jafari (r) is head of the
Islamist Dawa party
"Doctor Ibrahim al-Jafari was unanimously chosen," said Abd al-Aziz Hakim in a press conference.
The cleric, who led the United Iraqi Alliance to victory in the elections and heads one of the main Shia parties - the Supreme Council for the Islamic Revolution in Iraq (SCIRI), is closely affiliated to the religious clergy in Iran.
In a thinly veiled warning to al-Jafari, Allawi aide Imad Shabib warned that whoever filled the role would have "to behave as an Iraqi. He has to be loyal to Iraq and not to another country.
"Religion is a dangerous thing for Iraq. We don't want the Lebanese [civil war] story to be repeated here"
Aide to the Iraqi interim prime minister
"Religion is a dangerous thing for Iraq. We don't want the Lebanese [civil war] story to be repeated here. There are Shias and Sunnis in the same tribes, in the same families, but if we go down this road, we will create divisions," Shabib added.
Despite the religious Shia bloc commanding a majority, there may be staunch opposition from some seculars groups elected to the new parliament.