Abu Ghraib shot into notoriety after photographs of US prison guards torturing inmates at the facility just outside Baghdad surfaced.
While Saddam Hussein, Iraq's deposed leader, was in power, his administration held thousands of inmates at the prison.
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 pact which took effect on January 1, US forces in Iraq lost the power to hold without charge the approximately 15,000 detainees they have and are supposed to turn them over to Iraqi justice or set them free.
Ibrahim said the prison would house 3,500 inmates when it reopens in mid-February and would have a capacity for at least 15,000 by the end of this year.
"This prison will solve many problems for us - huge problems," he said.
Abu Ghraib is in an area where heavy fighting took place during the early years of the US invasion in Iraq. The US military closed the facility in 2006 after constructing a giant, purpose-built prison camp in the desert on the Kuwaiti border.