Prime Minister Haider al-Abadi had already declared victory on June 17 after IS defences collapsed, with Iraqi forces facing only limited resistance in subsequent clearing operations.
The offensive saw tens of thousands of civilians risk death to flee their homes, leaving Iraq to grapple with a humanitarian crisis as its forces prepare to attack the country's last remaining major IS hub of Mosul.
"This is joy for all Iraqis and it's the right of all Iraqi people to celebrate the retaking of Fallujah," Abadi said, speaking to Iraqiya state television outside Fallujah hospital.
Victory came when elite forces retook Jolan, a northwestern neighbourhood of Fallujah where the last holdout jihadists were holed up.
"It did not take more than two hours for CTS to retake Jolan," said Sabah al-Noman, spokesman for the counter-terrorism service that led the fight.
"Daesh (IS) did not fire a single bullet," he said.
Several other senior military commanders said only small pockets of IS fighters remained in the Fallujah area.
After a gruelling campaign, fighters rejoiced at the liberation of what was the first Iraqi city to fall out of government control two and a half years ago.
"Today, I am... very happy," said Mohammed Abed, a major with the rapid response force and a Fallujah native. "Fallujah is very beautiful... It is very unfortunate what happened to Fallujah."
Major blow to IS
The offensive began on May 22-23 with an initial phase aimed at tightening a months-old siege on Fallujah and led by the Hashed al-Shaabi, a paramilitary organisation dominated by Tehran-backed Shiite militias.
Qassem Suleimani, the powerful head of Iran's elite Revolutionary Guards' overseas operations arm, was more visible than ever before in Iraq during the early days of the operation.
The US-led coalition offered some aerial support but was less involved than six months ago during the operations to retake Ramadi, the capital of Anbar province in which Fallujah is also located.
The US had favoured focusing the battle on Mosul, the country's second city, where IS proclaimed a "caliphate" straddling Iraq and Syria two years ago almost to the day.
Wearing a scarf with the national colours around his neck in Fallujah Sunday, Abadi vowed: "We will raise the Iraqi flag in Mosul soon."
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The loss of Fallujah, which looms large in jihadist mythology and in 2004 saw US forces suffer some of their worst losses since the Vietnam War, is a blow to IS.
"The biggest victory achieved so far in the battle against Daesh is the battle of Fallujah," Hadi al-Ameri, a key Hashed al-Shaabi commander, told AFP there.
UN chief Ban Ki-moon called Abadi to congratulate him but also raised concerns over reports some forces had committed rights abuses against displaced civilians.
The jihadist organisation has lost several key leaders in air strikes, more than two thirds of the territory it controlled in Iraq two years ago and it faces multiple offensives in Syria.
Facing a seemingly inexorable decline of its de facto state, IS had reverted to old tactics and recently ramped up bombings against key infrastructure and civilian targets.
But few major attacks have been reported in Baghdad since the start of the Muslim fasting month of Ramadan.
The aid community was largely caught flat-footed however by the scope of the humanitarian crisis that resulted from mass displacement out of Fallujah.
According to the United Nations, 85,000 people were forced to flee their homes in the past month, leaving many crammed in hastily set-up camps with scant food or water.
The Norwegian Refugee Council, one of the leading groups that has provided assistance to the displaced since the start of the operation, has warned of an "impending disaster".
Lieutenant General Abdelwahab al-Saadi, the overall commander for the Fallujah operation, said limited damage had been caused to the city by the fighting.
"The percentage of destruction in Fallujah is no more than 10 percent," he told AFP.
That assessment is a massive improvement on the operation that saw Ramadi be retaken six months ago but also extensively destroyed.
Abadi said he hoped the displaced could return to their homes in Fallujah soon but the NRC and the United Nations warned the government should proceed with caution.
"We urge prudence and restraint in the communications with the displaced families as we have seen how, elsewhere, areas recaptured by Iraqi forces are still unsafe," NRC's Iraq director Nasr Muflahi said.