The Nato alliance is to assume control of military operations across the whole of Afghanistan from Thursday onwards.
An additional 12,000 US troops will come under Nato command
On 5 October it will take command of most US troops in the east.
The move will complete Nato's expansion across Afghanistan, making it responsible for peace-keeping and security across the country.
On Tuesday officials said two US troops and one Afghan soldier died in Kunar province. In Kandahar province at least one Nato-led soldier was killed.
Kunar, on Pakistan's border, is eastern Afghanistan's most troubled province. Three US soldiers were also wounded in the clash in Pech district.
"The soldiers were operating as part of a combat patrol that made contact with enemy extremists," a US military statement said.
The Nato-led International Security Assistance Force (Isaf) said as well as the soldier killed in Kandahar province, another was presumed dead.
A further eight had been injured when their patrol came under mortar and small arms fire in the province's Zhari district, a statement said.
International forces in the country's south and east are increasingly coming under attack from Taleban fighters.
"On the 5th of October Nato's Security Assistance Force will be expanded to all of Afghanistan," the alliance's senior civilian representative Dan Everts told a press conference in Kabul.
"Most of the US forces that are operating under their own command right now in the east will join the overall International Security Assistance Force (Isaf) organisation and be part of the unified Isaf Command," he said.
Isaf is the official name for the Nato-led force in Afghanistan.
Nato officials endorsed the expansion at a meeting of its defence ministers in Brussels last Thursday.
It means that an additional 12,000 US troops will come under Nato command.
Isaf - comprising 37 nations - took command of the Taleban-dominated southern provinces from the coalition on 31 July, moving into one of the most hostile areas of the country.
Correspondents say that British, Canadian and Dutch troops in the south have been engaged in some of the heaviest fighting since Nato's formation.
The aim of Isaf is to quell the spiralling Taleban insurgency through a dual mission of military pressure and reconstruction, intended to win "hearts and minds".
Nato troop numbers in Afghanistan now stand at 32,000, with around 8,000 US troops engaged in tracking down members of al-Qaeda in eastern Afghanistan.
They will remain under US command.
Correspondents say the expansion comes despite an admission from Nato military commanders that it does not have enough troops to carry out its mission.
It has appealed for member countries to provide another 2,500 troops.
Nato Secretary General Jaap de Hoop Scheffer recently warned it was very important for the alliance to stay in Afghanistan.
Nato says it needs more troops on the ground
The consequences of failure would be Afghanistan's return to "a hotbed of terrorism training and the violation of human rights", he said.
"We have to stay the course and we will stay the course - and we will prevail".
The Afghan and Pakistani presidents accuse each other of failing to act against the militants, with Afghan leader Hamid Karzai strongly criticising Gen Pervez Musharraf's peace deal with pro-Taleban militants in the North Waziristan border area.
Mr Karzai has also suggested that Pakistan has turned a blind eye to Taleban supporters using parts of the country to train and launch attacks on Afghanistan.
Gen Musharraf has angrily rejected allegations that his ISI intelligence service aided al-Qaeda and the Taleban.