Diplomats and relatives have been waiting for news
The Taleban has finally agreed to grant access to the eight detainees, who include two Australians, two Americans, and four Germans.
The aid workers, held on charges of illegally preaching Christianity, have not been seen by diplomats or relatives since they were arrested on 5 August.
Taleban Foreign Minister Wakil Ahmed Muttawakil told the Reuters news agency: "I have given the authorisation for the issue of visas."
According to the Australian foreign office, visas may be issued as early as Monday and the diplomats would fly into Kabul on Tuesday.
The announcement marks an about-turn from the Taleban who had refused to allow access to the arrested eight, or to 16 Afghan employees of the same aid agency, the Germany-based Shelter Now International.
Last week, diplomats from the US, Australia and Germany tried unsuccessfully to visit their nationals.
Pressure
Red Cross officials in Kabul have also confirmed that they had been given permission to see the aid workers - two Americans, four Germans and two Australians.
But spokesman Mario Musa was quoted as saying that the details of the visit still had to be finalised.
A Pakistan-based Afghan news agency said the ICRC could be allowed to visit the detainees on Sunday.
Diplomats suspected the Taleban were keeping the aid workers isolated to pressure them into confessing.
Foreign Minister Muttawakil said the visits were now possible because "the first important phase of the investigation is coming to an end."
The Taleban claims to have discovered bibles and Christian CD-roms in the local languages from the organisation's premises.
UN warning
United Nations Secretary-General Kofi Annan had accused the Taleban of violating international law by denying the detainees consular access.
Mr Annan warned that the continued detention of the aid workers could affect crucial humanitarian assistance to Afghanistan, which is suffering from the effects of war, poverty and drought.
The eight aid workers face trial under Taleban laws, although it is unclear which ones might apply to foreigners.
Two different decrees cover the crime of trying to persuade an Afghan to renounce Islam.
One applies to foreigners and orders deportation after a short prison term.
The other stipulates death for any Afghan who converts as well as the person who instigated the conversion.