WASHINGTON—Conditions in the western Iraqi province of Anbar, where a brutal insurgency once ruled, have improved so dramatically that the United States is handing over responsibility for security in the Sunni stronghold to Iraq within days. Troops freed up in Iraq could shift to Afghanistan.

“There aren’t a whole heck of a lot of bad guys there left to fight,” Gen. James T. Conway, the top Marine Corps general, said Wednesday.

A ceremony marking the Anbar turnover is expected to be held Monday, several U.S. and Iraqi officials said. Each spoke on condition of anonymity because the Iraqi government has not yet announced it. Anbar would be the 10th of Iraq’s 18 provinces to be returned to Iraqi government control, a step toward phasing out the American combat role as Iraqi security forces grow more competent.

The developments in Anbar have additional resonance because the province once was synonymous with the worst violence and lawlessness unleashed in Iraq.

The turnaround in Anbar is all the more dramatic for what it might mean for Afghanistan, the fight that has in some ways supplanted Iraq as a front-line battleground. The diverging trends make it likely that a U.S. buildup in Afghanistan will follow a drawdown in Iraq.