The vast base, built by the Soviets in the 1980s, is the biggest military facility used by US and NATO forces in Afghanistan, with tens of thousands of troops stationed there during the peak of America's military involvement in the violence-wracked country.
"I can confirm we will hand over Bagram Air Base," a US defence official told AFP without specifying when the transfer would take place.
An Afghan security official said the handover was expected in about 20 days and the defence ministry had set up special committees to manage it.
The base, the centre for nationwide command and air operations for the past two decades, also houses a prison that held thousands of Taliban and jihadist inmates over the years.
Washington has already handed over several military bases to Afghan forces before May 1, when it began accelerating the final withdrawal of troops.
Last month it completed the withdrawal from Kandahar Airfield in southern Afghanistan, once the second-largest foreign military base in the country.
The US withdrawal comes despite bloody clashes across the country between the Taliban and Afghan forces.
Peace talks were launched in September in Qatar, but so far have failed to strike any deal to end a war that has killed tens of thousands of people over nearly two decades.