The position has been empty since the bombing attack on UN headquarters in Baghdad last August that killed 22 people, including the head of the mission, Sergio Vieira de Mello.
Qazi, who has been in Washington for nearly two years, has been on Annan's short list for about a week along with Salman Haider, a former Indian deputy minister, and Surin Pitsuwan, Thailand's foreign minister, diplomats said.
Annan was to have made a decision two weeks ago but diplomats said his extensive travel this month was a prime cause for the delay. Earlier he had difficulty finding a qualified candidate because of the precarious safety conditions in Iraq.
Qazi served as Pakistan's high commissioner to India as well as Ambassador to China, Russia, the former East Germany and Syria. He has held diplomatic assignments in Copenhagen, Tokyo, Cairo, Tripoli and London. He has a master's degree in economics.
A special UN force is expected to guard UN staff, with diplomats saying fresh troops are expected from Nepal, Georgia, Ukraine and Azerbaijan. But the envoys said the United Nations was hopeful Pakistan would contribute to the force.
The UN Security Council's last resolution on Iraq in early June gave the United Nations a "leading role" in the country. It listed a long list of duties, including help to organise elections, reconstruction aid and judicial reforms.
But the council's resolution, at Annan's request, made a UN presence contingent on security conditions by adding the phrase, "as circumstances permit." It is unknown how large of a staff would go to Baghdad with Qazi.
"We want to respond constructively, but we do not want to scatter staff around the country if they are going to be vulnerable to hostage-taking or worse," Shashi Tharoor, UN undersecretary-general for public information, said earlier.
Pakistan Monday hailed the appointment of its ambassador to the United States, as the new United Nations envoy to Iraq, saying his years of diplomatic experience qualified him for the task.
"As ambassador Ashraf Jahangir Qazi will prepare to take this important and sensitive appointment, we wish him well and pray for his success," foreign office spokesman Masood Khan told AFP.
Khan said the assignment required quality of leadership which Qazi has amply demonstrated in his long diplomatic career.
The United States also welcomed the appointment of Ambassador Ashraf Jehangir Glazi to the post of UNSG's Special Representative on Iraq.
"We welcome it. We look forward to working with him at the United Nations, as we have worked with him in Washington as Pakistan's Ambassador."
The State Department Spokesman commented on the appointment of Ambassador Qazi for the important UN assignment.