About 400 prisoners are currently being held there on a trial basis.
Abu Ghraib earned global notoriety after photos released in 2004 showed US prison guards sexually humiliating inmates at the facility, less than a year after the 2003 US-led invasion that toppled Saddam Hussein.
Busho Ibrahim, Iraq's deputy justice minister, said last month the Abu Ghraib prison had been renovated to meet international standards.
"We have named it Baghdad Central Prison because of its bad reputation as Abu Ghraib prison, not just because of what the Americans did there but also because of what the regime of Saddam has done," he said.
While Saddam. Iraq's deposed leader, was in power, up to 60,000 inmates were held in the prison.
The US military closed the jail in 2006.
Iraq has been under pressure to increase the capacity and quality of its prisons and improve the transparency and efficiency of its criminal justice system.
Under a bilateral security agreement, according to which the US will withdraw its troops from Iraq by the end of 2011, the US military has to hand over around 14,000 Iraqis it is holding after detaining them as suspected fighters or militia members.
Most of those detainees are expected to be freed without charge but some will face trials under Iraqi law.
Iraq's prisons are already overcrowded and human rights groups such as Human Rights Watch and Amnesty International say prisoners in Iraqi custody are often beaten, abused and denied due process.