"We aim for these deployments to be fully operational by July this year," John Reid, the British defence secretary, told parliament on Thursday.
The new troops include a Provincial Reconstruction Team for Helmand province in the south and for fighting the drug trade.
Reid said more than 1000 troops will be sent to the Kabul headquarters of the Allied Rapid Reaction Force, whose command Britain assumes from May until February 2007.
He acknowledged the forces faced risks in a part of Afghanistan where the Taliban, which ruled the country until US-led forces overthrew it in 2001, remained active and the influence of drug traffickers was strong.
Clutches of Taliban
But Reid added: "Those risks are as nothing compared to the dangers to our country and our people of allowing Afghanistan to fall back into the clutches of the Taliban and the terrorists."
The announcement of the one-billion pound deployment followed "a unanimous decision" by Tony Blair's cabinet, the British prime minister's official spokesman said earlier.
British soldiers will deploy at a
time of rising Taliban attacks
Troop numbers will fluctuate over three years and will not affect Britain's deployment in southern Iraq, Reid said.
British media outlets had speculated that between 3000 and 4000 British troops would be sent to Afghanistan in addition to the 1100 already there.
Blair's spokesman said British involvement in Afghanistan was both a military operation and one to rebuild the country's infrastructure to prevent a "slide back" to the Taliban "and all the implications of that".
"[The UK cannot allow]Afghanistan to fall back into the clutches of the Taliban and the terrorists"
British Defence Secretary
It was also "to recognise the importance of Afghanistan in terms of the drugs war here on our streets".
The UK spokesman added: "It's the case that 90% of heroin sold on our streets comes from Afghanistan".
The announcement on commitments of British forces had been long awaited in advance of Britain's assuming command of the Nato International Security Assistance Force in Afghanistan later this year.