US Defence Secretary Ash Carter said there was "still some fighting to be done" as IS fighters are still in control of certain parts of the city. But Iraq's prime minister hailed the day's events as a "liberation".
A senior army spokesperson said he expects IS to "suffer a total breakdown during the next hours".
"The enemy is collapsing. They have lost control of their fighters. They are on the run now," Lt Gen Abdul Ameer al-Shammari said.
Special forces commander Brig Haider al-Obedi told that the government forces are now in control of 80% of the city. Iraqi army officials are willing to allow the IS militants a path out of the city in order to avoid heavy fighting in areas populated by civilians.
Falluja is located 50km (30 miles) west of Baghdad. It has been held by IS for longer than any other city in Iraq or Syria.
Iraqi forces were backed by air strikes from the US-led coalition in their fight to retake Falluja. Iraqi Prime Minister Haider al-Abadi said on state TV: "We promised to liberate Falluja, and we took it back. Our brave forces went into Falluja and took control of the city centre. There are still some pockets that need to be cleared in the next few hours".