In a tribute to all the British casualties since 2001, Mr Browne added: "They gave their lives securing freedom and stability, not just for the people of Afghanistan but, as the tragic events of 9/11 showed, for all of us. We will never forget them."
He said that British troops had "transformed" the heartland of the Taleban from an area of lawless oppression and terrorism to a place of democracy and development.
Air Chief Marshal Sir Jock Stirrup paid tribute to 100 "brave and professional servicemen" who had died.
He said he reflected on the most recent deaths with "both a sense of deep sadness and pride", saying the military effort was starting to achieve real change.
Sir Jock, who is Chief of the Defence Staff, said: "Every one of those deaths is a tragedy.
"Nothing can ever compensate for the loss felt by their loved ones and to them all I extend my deepest sympathies.
"I only hope that the terrible hardship that they have been asked to bear can be eased by the certainty that in Afghanistan our forces are engaged in a most worthy and noble endeavour."
The BBC's defence correspondent, Paul Adams, says some will question Mr Browne's and Sir Jock's "optimistic" assessments that British troops are helping to turn the tide of the conflict.
"With the country's central government weak and corrupt and Taleban influence still felt in much of the south this war has a long way to go," he said.
Conservative party leader David Cameron said the country owed "so much" to the servicemen and women fighting in Afghanistan.
"The death toll having now reached 100 serves as a tragic reminder of how brave and courageous they are."
Liberal Democrat leader Nick Clegg said that the cause for which the soldiers died was "a just one."
He added: "The consequences of failure in Afghanistan would be unimaginable - a boost to terrorists who seek to harm our way of life, an increase in hard drugs on our streets and terrible instability in an already unstable region."
Conservative MP Patrick Mercer, a former commanding officer in the British Army, told the BBC that it was time Nato member states began committing more of their forces to combat operations in southern Afghanistan.
He said: "I hope very much that our allies will continue to bear more of the burden than they have done in the past, particularly in things like close air support and artillery support.
"Our infantrymen and our armoured soldiers and our sappers are fighting a hard and difficult battle, and they need as much international support as they can possibly get."
Of the 100 personnel killed in Afghanistan since 2001, 74 have died as a result of hostile action.
The remaining deaths were caused by illness, accidents and non-combat injuries, or else their causes have yet to be formally classified.
The parents of Captain David Hicks, killed in Afghanistan in August 2007, remember their son
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