Quantock says most of the prison’s detainees are low and midlevel insurgents who are held on warrants. Only a small number have been convicted.
The handover comes as the U.S. prepares to withdraw all combat troops from Iraq by September, and all troops by 2012.
The Taji prison lies inside an American base with the same name, 12 miles north of Baghdad.
The U.S. plans to hand over the remaining prison, Camp Cropper, in July. About 100 of its 2,900 detainees will remain in U.S. custody.
Meanwhile, early election results show incumbent Nouri al-Maliki pulling ahead following pivotal national elections which Iraqis hoped would end years of sectarian strife. The narrow vote suggests that a long period of talks will be needed before a new government may be formed.
The results are still incomplete more than a week after the vote. Prelimary tallies released so far represent just over a quarter of 12 million votes cast, and may change, according to Reuters.