Germany has offered to contribute 1,000 troops
"I am pleased that the United Kingdom is willing to step forward and volunteer for a leadership role," he said in Paris after talks with President Jacques Chirac and Foreign Minister Hubert Vedrine.
The first official announcement of the UK's role is expected after Mr Powell arrives in London shortly, on the final leg of an eight-day tour of Europe and Central Asia.
Both France and Germany have confirmed that they are also willing to take part in the stabilisation force, with Germany offering 1,000 soldiers.
Mr Powell said that the next step would be "to get a UN resolution in place" to formally set up the force.
In Berlin on Monday evening, Mr Powell stressed that the force would be completely separate from the US operation in Afghanistan to track down the leadership of Osama Bin Laden's al-Qaeda network.
"They are two completely different missions. Obviously there will have to be some co-ordination," he said.
Italy, Canada, Turkey and Jordan are also expected to contribute to the 5,000-strong force.
Kabul security
Its formation has been delayed because of a desire by the US military to maintain overall control, while Britain and Germany have insisted that unless the US contributes troops, it cannot lead the force.
Countries contributing troops will meet in London in the next few days to decide how and when to deploy the force.
Its goal is to provide security in Kabul and the surrounding area in order to provide protection for the new coalition government, for example by preventing any one military faction taking over.
It could then be expanded to other areas, according to agreements reached in Bonn.
Some had favoured Germany to lead the force, because unlike the UK it has no colonial baggage in Afghanistan.
The British command is expected to last up to six months.
Jordan is also likely to contribute troops, and Bangladesh if it can find the funds to finance the mission.