Gen Joseph Dunford told reporters the decision will allow an advisory force of 9,800 troops to remain in the country to finish training and equipping Afghan security forces.
"I believe that this decision was good news for the Afghan people," Dunford said. "It eliminates the uncertainty about the future here in Afghanistan, in the region and within the coalition."
He added that it "also sends a message to those who said that Afghanistan would be abandoned at the end of the year and that simply isn't true. "
NATO and other US allies also are expected to commit troops, bringing the total to be around 12,000.
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Some American troops are also expected to play a counterterrorism role, chasing any elements of al-Qaida and other such groups still operating in Afghanistan.
The commitment is conditional on Afghanistan's government signing a stalled bilateral security agreement. While Afghan President Hamid Karzai has refused to sign it, both the candidates running to replace him former Foreign Minister Abdullah Abdullah and ex-Finance Minister Ashraf Ghani Ahmadzai have said they will.
More than USD 4 billion to equip, train and pay the Afghan security forces through 2016 is also contingent on signing the agreement. A failure to fund the Afghan security forces likely would have meant their rapid dissolution in the face of an insurgency that shows no signs of weakening or abating.
The Taliban today said that Obama's announcement did not mean an end of the war, promising to keep fighting until the last foreign soldier leaves.