Stoltenberg told a news conference in Brussels on November 7 that the troops would not have combat roles but would be part of NATO's "train, advise, and assist" mission called Resolute Support.
Half the additional troops will come from the United States and the other half from other members of the 29-nation alliance and partner countries, Stoltenberg said.
Allies are expected to commit troops during two days of NATO defense ministerial talks starting in Brussels on November 8.
The additional NATO troops would take Resolute Support's total to around 16,000 troops, up from around 13,000 today, Stoltenberg said.
"We have decided to increase the number of troops...to help the Afghans break the stalemate," Stoltenberg said.
Stoltenberg said there will also be more help to develop the Afghan Air Force.