The Islamic State group flag flying over Iraq's Fallujah is in tatters and its fighters are dead or gone, leaving behind a broken city of bomb-rigged buildings and empty streets.

Only scattered signs of IS's self-declared "caliphate" remain in Fallujah, a city west of Baghdad that was seized by anti-government fighters in early 2014 and later became a key jihadist stronghold.

The story of Fallujah's de facto independence from Baghdad, which some Sunnis initially hailed as liberation from a discriminatory government, has ended in mass displacement and destruction from which it will take years to fully recover.

Fallujah's broad streets are empty except for members of the security forces, some relaxing or firing in the air to celebrate their victory, while others search for bombs that are one of IS's legacies in the city.

Police detonated a massive cache of explosives in a house in central Fallujah, sending a towering cloud of dust rising over the city and spraying debris across the neighbourhood.

The house had "five tonnes of ammonium nitrate" inside and was rigged to detonate if someone tampered with the explosives, said Colonel Nabil Radhi of the federal police.

Security personnel walked down another empty street, searching for bombs in buildings so they could be dealt with later.

- Burned prisons, court -

Most of IS's black flags have been removed, but the torn remains of one still fluttered from a street light in Fallujah.

IS flags are also painted on support pillars and murals under an overpass in Fallujah, but they have been daubed with red paint, and graffiti with the names of Iraq's elite counter-terrorism service and a militia umbrella group makes the city's change of ownership clear.

Iraqi forces discovered multiple IS prisons and at least one court in the city.

A prison located inside one house, which had heavy metal gates blocking off rooms inside, was set on fire by the jihadists, said Second Lieutenant Hussein Shaker of the interior ministry's rapid response forces.

Security personnel held in the prison were burned alive while IS fighters fled, Shaker said.

Another house -- this one said to have been burned by Iraqi forces -- contained seven metal cages, some of them not even large enough to stand in.

Other remnants of IS's rule are also still in evidence: security forces showed AFP a marriage document issued by the jihadists, and one building was marked as their "Agricultural Centre of the State of Fallujah."

Another document said that songs, television programmes and films were banned, while a large sign said women should be completely covered from head to foot.

- Makeshift boats, shaved beards -

The IS fighters still in Fallujah are dead, some of them decomposing in the searing summer heat amid rubble at the site of an apparent air strike.

Bodies of dead fighters also lay in the courtyard of what was once a school, while more were said to be buried below.

But other jihadists managed to flee the city, with some fighters shaving their long beards to aid their escape.

"We found a mountain of their beards" in one house, Shaker said.

Small makeshift boats constructed from corrugated metal with low wood transoms were left at the same school where the bodies were located, apparently intended for crossing the Euphrates River to safety.

Parts of Fallujah are relatively untouched, with houses only scarred by bullets or shrapnel if they are damaged at all.

But others have been smashed by air strikes or shelling, while many more houses and shops have been set on fire by either IS or Iraqi forces.

Anti-government forces seized Fallujah in 2014 amid widespread anger among its Sunni Arab residents, who felt marginalised and targeted by the Shiite-led government in Baghdad.

But instead of a better life, residents suffered over two years of IS rule that led to siege, privation and fighting that forced them to flee and ultimately put the city in the hands of some of the very forces they feared.