The US military currently has 28,000 soldiers in Anbar, down from 37,000 in February, according to US figures, while the number of Iraqi soldiers and police has reportedly risen to 37,000, from 5,000 three years ago.
Falluja once had a reputation for lawlessness and brutality
"Our forces are ready to take the security responsibility," Majid al-Assafi, Anbar's new police chief, told AFP news agency. "They are controlling the situation."
The handover of Anbar was postponed several times. Initially scheduled for March, the transfer was delayed until June before being pushed back again.
US officials blamed June's delay on a sandstorm and then another hold-up in July on a disagreement between the province's governor and the Iraqi government in Baghdad over the control of security forces.
Following the 2003 US-led invasion, many members of Anbar's Sunni tribes turned to al-Qaeda in Iraq and other insurgent groups.
The ambush of four US contractors in the Anbar town of Falluja in March 2004 - whose burned corpses were dragged through the streets - was a low point for American efforts to pacify the province.
But in late 2006, Anbar began a dramatic change after Sunni tribal leaders turned against al-Qaeda, accusing the movement of attempting to dominate the insurgency.
The Sunni tribal leaders formed "Awakening Councils", and began to take charge of security. Once the councils emerged, the US military backed the with money and weapons.
Anbar became a much less dangerous place, but the Awakening Councils remain a separate military and political force in the country.
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