The reinforcements, approved by US President Barack Obama last week, will head mainly to the southern provinces of Helmand, Kandahar and Zabul although details were being finalised, Lieutenant General Jim Dutton told reporters.
They will secure the border with Pakistan and "thicken up the force ratios in those areas where the insurgency is still at its most virulent," the International Security Assistance Force (ISAF) deputy commander said.
"There are lots of pretty stable pockets in both those areas. What we have not managed to do is to join them up to widen and deepen the security to allow complete freedom of movement," the British soldier said.
An extra 120 helicopters, which have also been approved, will provide extra mobility to the troops and prove "game-changing", he said.
There are already about 70,000 foreign troops in Afghanistan, in ISAF and a separate US-led coalition, helping to fight against a Taliban-led insurgency that saw record attacks last year and to build up Afghan security forces.
ISAF commander US General David McKiernan had asked for reinforcements of 17,000, Dutton said, despite reports that up to 30,000 were needed.
They will arrive "basically as fast as they can reasonably be deployed here", he said.
ISAF has also asked contributing nations for more soldiers and helicopters to secure presidential elections due in August.
"We are probably talking about thousands (of soldiers) but not many thousands," he said. "This is to provide some extra mobile forces available on one day, maybe two days, to provide security should it be required."
"We are confident here that we will get what we have asked for," Dutton said. Finland and Germany are among nations that have already pledged troops for the vote, Afghanistan's second presidential election.
The commander said there had been a "considerable downturn" in insurgent activity in the east in the past three months that may be linked to increased Pakistan pressure on rebel bases.
The east and south have been the main battlefields in Afghanistan since the US-led invasion in 2001 ousted the Taliban regime for sheltering Al-Qaeda.