The decision on Monday was another step towards improving relations with Washington that were strained when Turkey refused to allow US troops to stage an invasion of Iraq from Turkish territory in March 2003.
A cabinet decree - allowing the US to fly more cargo planes to the southern Incirlik air base for one year beginning in June - was sent to President Ahmet Necdet Sezer for approval, the semi-official Anatolia news agency said.
The details of the agreement were not released. Washington's request, which was relayed to Turkey in June, asked permission to establish a logistics hub at Incirlik.
US ambassador Eric Edelman and Turkish Defence Minister Vecdi Gonul are scheduled to hold a joint news conference on the deal on Tuesday.
According to private NTV television, Turkey also accepted a Pentagon request for blanket clearance for all cargo flights, backing off an earlier stance that each flight should get separate permission before landing and takeoff.
US diplomats had expressed unease about Turkey's delay and its insistence on requiring separate permission for each flight.
Need for base
The US plans to fly in large civilian cargo flights to Incirlik and redistribute the goods to military planes for Afghanistan and Iraq.
Incirlik now hosts 10 KC-135 refuelling aircraft, supporting operations for Afghanistan and Iraq. There are about 1400 airmen at the base.
The current deal expires on 23 June. The one-year mandate of the new agreement will very likely start then.
Turkey last year allowed the US to fly thousands of its troops out of Iraq through Incirlik, which is about 1000km from the Iraq border and 3200km west of Afghanistan.
Washington has had access to Incirlik since 1954. It and its allies used Incirlik during the 1991 Gulf war to launch air strikes against Iraq. It was also the hub for US-led flights enforcing a no-fly zone over Iraq for 12 years until 2003.