Anbar, however, is the first predominantly Sunni district to be moved to Iraqi security, and home to about two million people.
The province is Iraq's largest, stretching from the border with Jordan to the capital, Baghdad. Much of it is desert, but it has seen some of the heaviest fighting since the US occupation.
Tens of thousands of Iraqi and US troops are working in the area and about one third of all US combat deaths have occurred in Anbar, where there was heavy fighting against the US-led forces particularly in Falluja.
Majid al-Assafi, the head of the province's police force, said: "Our troops are on alert to avert any failure of the transfer."
Before the handover, US forces increased their patrols in Ramadi, the provincial capital.
There are 28,000 US soldiers in Anbar at present, down from February when the US put the figure at 37,000.
Three years ago there were 5,000 Iraqi soldiers, a deployment that has now grown to 37,000.
Reducing troop numbers in Iraq will allow the US to redeploy to Afghanistan, a move encouraged by Democratic presidential hopeful Barack Obama.
Some US troops will remain and will carry out training as well as participate in military operations when required.
Iraq and the US have so far failed to agree a timetable for withdrawal, with some critics remaining unconvinced that a handover will be successful.
One resident said: "Our forces are not ready to take responsibility for the situation. There is a lot of corruption in our security forces."
US and civilian casualties started to decline in the province after the creation of so-called "Awakening Councils", local tribal groups who are funded by the US.
The handover was originally due on June 28.
PHOTO CAPTION
Iraq map locating Anbar province
Al-Jazeera