Surprise and confusion reigned in both Washington and at the UN on Friday as word spread over the announcement.
US officials initially hesitated to confirm Allawi's appointment for a period of three hours after the announcement.
White House spokesperson Scott McClellan emerged later and said Allawi "is certainly a fine and capable leader who appears to have broad support among the Iraqi people."
"There was a meeting of the Governing Council and Dr Allawi was unanimously chosen as prime minister," said Hani Idris, an aide to Allawi.
UN officials hinted Allawi's selection by the Iraqi Governing Council had come as a surprise to al-Akhdar al-Ibrahimi, UN special envoy to Iraq, although they said Allawi was "high on his list" of choices.
When reports indicated al-Ibrahimi had not been present when Allawi was selected, McClellan said: "But I want to be respectful of that process and we'll wait until we here more from Mr al-Ibrahimi."
"Mr al-Ibrahimi respects the decision and is prepared to work with this person on the selection of the other posts in this interim government," UN chief spokesman Fred Eckhard said.
The word "respects" had been "a carefully chosen word," Eckhard said, declining to say whether al-Ibrahimi "endorsed" Allwai or had helped choose him.
"The Iraqis named this person today, and Mr al-Ibrahimi respects that decision and will work with that person to now name the other members of an Iraqi government," Eckhard told reporters, adding that UN Secretary-General Kofi Annan also respected the choice of Allawi.
"I assume this choice will hold, but the process isn't over yet," he added.
'Not exactly as planned'
Eckhard acknowledged the process was not unrolling as the United Nations had envisioned, but said such decisions were ultimately up to the Iraqi people and the US-led occupying authority.
Al-Akhdar al-Ibrahimi stopped
short of endorsing the PM choice
UN spokesperson Ahmad Fawzi said al-Ibrahimi and the UN were never meant to appoint the government, but help Iraqis identify candidates.
"We were not invited to appoint the government," Fawzi said. "Now that it has been identified, we welcome the choice. We will be working with the prime minister-designate to appoint a Cabinet, two vice presidents and a president."
The interim government will take over running the country from the United States on 30 June. Al-Ibrahimi is helping select a 30-member team, including a president and 26 ministers.
Comments from the UN came only after a series of US officials had told reporters that as far as they knew, the selection process was not yet complete.
"We have no position on any candidate at this moment because we are waiting to hear from Ambassador al-Ibrahimi and he needs time to complete his work," said Secretary of State Colin Powell on Friday.
Allawi, a wealthy secular Shia Muslim and former member of Saddam Hussein's Baath Party, is a relative of Ahmad Chalabi, a former Pentagon favourite who has fallen out with Washington, but the two are not regarded as particularly close.
Chalabi was himself long seen as Washington's likely choice to lead post-Saddam Iraq.
Allawi, a British-educated neurologist, went into exile after turning against Saddam and in 1990 formed the Iraqi National Accord, a party backed by the CIA and British intelligence and including many former Baathists who fled the Baghdad regime.
He was injured in an assassination attempt in London in 1978. The attack was believed to have been ordered by Saddam Hussein, but no evidence has emerged to support this claim.