"The European NATO allies will contribute, temporarily, in smaller numbers," he said.
"[Obama said] that there would be 5,000 troops and trainers, 3,000 of that will be actual combat troops, the largest contingent of that force will be ... from Britain."
Robert Gibbs, the White House spokesman, said 900 troops will come from the UK, 600 from Germany and 600 from Spain.
Italy and France would also commit forces, he said.
Speaking about Afghanistan earlier on Friday, Obama had said that "Europe should not simply expect the United States to shoulder that burden alone".
Shortly after taking office in January, Obama pledged to send 21,000 more troops to Afghanistan and is reportedly considering sending 10,000 more.
More than 70,000 foreign troops are already stationed in Afghanistan.
Both Angela Merkel, the German chancellor, and Nicolas Sarkozy, the French president, met Obama before the summit got under way.
Speaking at a news conference with Obama on Friday, Sarkozy gave his support to "the new American strategy in Afghanistan".
He said France, which has just been admitted back into Nato's military command structure after a 43-year absence, was "ready to do more" in the field of police training and economic aid, but had initially been tentative about increasing troops.
Merkel, the summit's co-host, said after talks with Obama in Baden Baden in Germany: "We have a great responsibility here. We want to carry our share of the responsibility, militarily, in the area of civil reconstruction and in police training."
"[The Obama administration's approach to Afghanistan] complements fully what Germany has in mind - a comprehensive approach,'' she said.
Following the end of the Nato summit on Saturday, Obama headed to Prague, the Czech capital, where he will meet with EU leaders over the weekend.