The handover of security in Afghanistan to its own armed forces is a "hard-fought milestone", Defence Secretary Philip Hammond said.
The handover marks a turning point for coalition forces, which will now move into a supporting role, and paves the way for full withdrawal in 18 months.
Mr Hammond said the announcement meant Afghan National Security Forces are in control of security throughout the country and for all of its 27 million citizens.
"This is a hard-fought milestone on the road to complete Afghan security responsibility, with Isaf (International Security Assistance Force) forces now moving to a role of training, advising and assisting," he said.
"The Afghanistan our combat forces leave at the end of 2014 will not be perfect, but will be able to stand independently and will never again provide a haven for terrorists to attack the West. That is why we remain firmly committed to supporting Afghanistan beyond 2014 and into the future."
Mr Karzai announced the security handover at a ceremony at the new National Defence University in Kabul - as a bomb attack in another part of the capital left at least three people dead.
Lieutenant General Nick Carter, the UK's most senior officer in Afghanistan, said insurgents remain capable of mounting "spectacular attacks" but insisted Afghan forces were "quite capable of seeing them out".
The deputy commander of Isaf told BBC Radio 4's The World At One: "The insurgency still have the capacity to mount spectacular attacks in Kabul and in other Afghan cities. However, what gratifies us is that the Afghans are able to deal with this on their own now. Their intelligence systems are improving significantly."
Asked if he expected an upsurge in Taliban violence, he replied: "Absolutely, I would. These campaigns are always about the competition for people's minds, they are all about perception, and the Taliban would very much like to give the impression they are driving the international community out of Afghanistan and, of course, that they are prevailing in their military campaign. The reality is they are not doing as well as they might think and it is going to become increasingly difficult for them to persuade Afghans to fight Afghans."
https://www.gov.uk/government/ministers/secretary-of-state-for-defence(Defence Secretary Philip Hammond)