The announcement came from Iraq's Prime Minister Nuri al-Maliki in a televised news conference Thursday in Iraq.
"Today Zarqawi has been terminated," Maliki told a televised news conference, prompting Iraqi journalists in the room to burst into applause.
Maliki, whose fledgling government was boosted by the news of Zarqawi's death and the confirmation of key Cabinet positions on Thursday, added, "Every time a Zarqawi appears we will kill him."
General George Casey, the top U.S. general in Iraq who joined Maliki at the press conference, told reporters Thursday that Zarqawi's body has been identified by fingerprints and facial recognition.
Al-Qaida in Iraq confirmed the death of its leader in a posting on an Islamist Web site.
"We herald the martyrdom of our mujahed (warrior) Sheikh Abu Musab al-Zarqawi in Iraq... and we stress that this is an honor to our nation," a statement signed by Zarqawi's deputy, Abu Abdulrahman al-Iraqi, according to Reuters.
"We tell our prince, Sheikh bin Laden, your soldiers in al-Qaida in Iraq will continue along the same path that you set out for Abu Musab al-Zarqawi," said the statement, which could not be immediately authenticated.
American Special Forces conducted the air strike that killed Zarqawi, targeting the militant's location north of the troubled city of Baquba north of Baghdad.
In Jordan, military officials confirmed Zarqawi's home nation's intelligence agents had helped coordinate Wednesday's raid.
"There has been early exchange of intelligence information with the United States that helped in the operation that killed Zarqawi," government spokesman Nasser Joudeh told Reuters.
Maliki added that other intelligence had been supplied by residents in the area, and U.S. forces acted on the information.
In Washington, President Bush hailed the death of the Jordanian-born militant.
"Now Zarqawi has met his end, and this violent man will never murder again," the president said in the Rose Garden, adding Americans "can be justly proud" of U.S. soldiers in Iraq.
British Prime Minister Tony Blair also welcomed the news, telling his Cabinet, "Today's announcement was very good news because a blow against al-Qaida in Iraq was a blow against al-Qaida everywhere," Blair's office said in a statement.
But the American president also cautioned that the death of its leader would not end the work of al-Qaida in Iraq.
"Zarqawi is dead, but the difficult and necessary mission in Iraq continues," Mr. Bush said. "We can expect the terrorists and insurgents to carry on without him. We can expect the sectarian violence to continue."
Blair echoed the president's sentiments, telling reporters, "There will be fierce attempts, with the formation of the government, with the death of al-Zarqawi to fight back."
Their words were grimly confirmed later Thursday when two bombs went off near a market and a police patrol in Baghdad, killing at least 19 and wounding more than 40.
As the head of al-Qaida in Iraq, Zarqawi emerged as the most visible and brutal leaders of the ongoing insurgency against the Shiite government of Iraq and the American military presence in the country.
In his last public statement, Zarqawi called on all Sunnis to attack Shiites, labeling believers in that branch of Islam infidels. Several of Zarqawi's attacks had appeared to target Shiites in an effort to fuel civil war in Iraq, including attacks in Samarra that prompted widespread violence that killed hundreds in February.
Although it was often Zarqawi's group behind the attack, the Jordanian also took a personal hand in some of the bloodiest scenes of the insurgency, personally beheading American Nick Berg and others on videotape.
In Jordan, Zarqawi had been sentenced to death three times for his militant attacks that killed an American diplomat and failed plots to attack Israeli and U.S. targets in and around the capital of Amman.
The U.S. government had also put a $25 million bounty on Zarqawi's head due to his continued attacks against American forces and civilians in the war-torn nation.