Media reports on Friday suggested that more than 1,000 extra troops will be sent.
Browne did not specify a figure or say when they would go but a statement was to be given to parliament on Monday.
ISAF has 32,000 troops in Afghanistan but troops from countries including Britain, the US, Canada, Denmark and the Netherlands have borne the brunt of violence in the south.
“We have been trying hard to get other nations to live up to the joint commitment Nato made to Afghanistan and provide more forces, forces which are authorised to fight,” Browne said in a statement.
“We will continue to press. But we must be realistic. We have decided that it is right for the United Kingdom to provide some additional forces for the southern region.”
Britain has the second-largest contingent in the 37-nation Nato-led International Security and Assistance Force (ISAF) and has already increased its troop numbers several times.
With a renewed spring offensive from the Taliban expected, Browne said more troops were vital in places like Helmand but a lack of reinforcements put at risk gains made since the Taliban were ousted from power in 2001.
The confirmation comes two days after Tony Blair, the UK prime minister, said 1,600 British troops in southern Iraq will be withdrawn in the coming months.
Opposition politicians suggested the reduction was announced because it was the only way for an over-stretched military to reinforce its numbers in Afghanistan.
But both Browne and James Appathurai, the Nato spokesman, rejected any link.
A senior Taliban commander said on Friday that British forces would face “hundreds” of suicide attacks in Afghanistan and that they welcomed any increase in the Nato presence.
“We don’t care,” said Mullah Dadullah. “More troops means more will be killed. And that would make us happy. We’re happy for them to come.”
Another Afghan regional commander, believed to be loosely allied with the Taliban, has said that the US will soon be forced to withdraw its troops from Afghanistan and Iraq.
Gulbuddin Hekmatyar, leader of the Hizb-i-islami armed movement, blamed the US for Afghanistan’s problems, in a tape obtained by Reuters news agency and released on Thursday.
Hekmatyar, a former prime minister whose forces operate in southeastern areas near Pakistan, denounced the US as “the mother of problems”.