A transfer ceremony is set to take place at Bagram prison, now officially known as the Parwan detention centre.
It had been delayed while the two sides finalised a deal over the fate of prisoners considered dangerous.
Bagram jail has been at the centre of a number of prisoner abuse allegations.
It was once located in Bagram air base, one of the largest military bases for Nato-led forces in Afghanistan, about 40km (25 miles) north of the capital, Kabul. The new Parwan facility was constructed a few miles away and populated with inmates in 2010.
Last March the US agreed to hand over responsibility for the majority of the detainees, thought to number more than 3,000, and actually held a transfer ceremony last September.
1979-88: Key base for troops and supplies during Soviet occupation
2001: Air base taken over by coalition forces following fall of Taliban regime, also becomes the main US detention facility in Afghanistan
July 2005: Escape by four "dangerous enemy combatants", the first by any prisoners
February 2007: Suicide attack outside base during visit by US Vice President Dick Cheney kills more than 20 people
2010: Thousands of prisoners moved to Parwan Detention Centre, built outside base with extra capacity to replace old prison
April 2010: Allegations surface of prisoner abuse at a hidden facility at Bagram
February 2012: Violent protests erupt after US troops inadvertently burn copies of the Koran at Bagram - at least 30 are killed
March 2012: Agreement to hand over jail to Afghan control
September 2012: Handover ceremony held but US forces remain to guard a core of "dangerous" prisoners
March 2013: Final handover ceremony cancelled by US over concerns over fate of those prisoners
But the full transfer was held up over a disagreement about the fate of certain inmates who the US feared could be released if the prison was handed over.
US forces remained at the prison and continued to guard about 50 inmates as well as those taken into custody since the initial transfer deal, AFP news agency reports.
Earlier this month a ceremony transferring the final prisoners to Afghan custody was called off at the last minute because Afghan President Hamid Karzai reportedly rejected part of the deal.
The Pentagon says an agreement has now been reached and reports say this ensures that prisoners of concern will not be released from the detention centre without a full review.
Bagram prison has earned a chequered reputation over the past decade. It has been described as "Afghanistan's Guantanamo".
In January 2012, Afghan investigators accused the US Army of abusing detainees at Bagram. The investigators said prisoners had reported being tortured, held without evidence and subjected to humiliating body searches.
Nato and the US have rejected allegations of abuse as untrue and pointed to the fact that they have given the Afghan Human Rights commission access to check them independently.
In February 2012, US soldiers unwittingly burned Korans confiscated from prisoners at Bagram, leading to days of protests and targeted killings across Afghanistan.
A US investigation said there was no malicious intent to insult Islam.
But the future of the US-run prison had become a thorn in the side of US-Afghan relations ahead of the planned withdrawal of these forces in 2014.
Many Nato forces have already begun withdrawing troops from Afghanistan ahead of the complete transfer of power to Afghan security forces.
