Abdel Karim Berges said on Wednesday he had put in his papers after his sons, aged 15 to 30, were freed in Falluja following one week in captivity.
Berges said he had paid no ransom but met the captors' demand that he leave office.
Ramadi's chief administrator Mohammed Abed Awad has taken over his duties.
The three sons of Berges were taken captive by armed fighters who barged in and torched his family home in Ramadi while he was at work.
Ramadi, 100 west of Baghdad, is the capital of the Sunni Muslim governorate of Anbar, which also includes the city of Fallujah where US troops have come under repeated attack and loyalty to Saddam Hussein remains high.
Also on Wednesday, reports Aljazeera's correspondent in Ramadi, a car bomb exploded near a US checkpoint at the eastern entrance of the city.
The blast, which targeted a US patrol, left a number of casualties among the US forces and damaged a military vehicle, the correspondent said.
Earlier, during an overnight raid US occupation forces arrested an Iraqi police colonel and searched a police station in Ramadi, police sources said.
"An American unit went to the home of Colonel Imad Suleiman Falah at 2:30 am (2230 GMT) and arrested him without explanation," said policeman Ziya Hadi.
US soldiers also searched the al-Faruq police station in the centre of Ramadi for more than three hours, Hadi said.
A US military spokesman in Baghdad said he had no information about the reports.
US commanders in Iraq have become worried of late about reports suggesting that anti-occupation individuals and members of Iraq's disbanded army and security forces have been implanted inside the US-trained Iraqi police.
Last week, armed Iraqi fighters inflicted heavy losses on Iraqi police and US forces in a battle that took place in al-Swaira.
The US army later said the fighters were surprisingly well organised in the way they fought, indicating that they had probably been tipped off.
Five Iraqi policemen were killed in that battle, but no information was available to Aljazeera's correspondent in the city about US casualties.