"Members of the Taliban who give up their fight are being paid 100 pounds a month and will be allowed to keep their guns in a new initiative to end the insurgency," the Sunday Telegraph newspaper reported.
The move, which has the full support of NATO, is part of the "reintegration" programme and is intended to keep militants from attacking troops from the International Stabilisation and Assistance Force (ISAF).
"Those who have attacked and killed British forces are also effectively given an amnesty, which means they will never be put on trial," the paper said.
Maj Gen David Hook, the director of the Joint Force Integration Cell in Kabul, told the paper the programme would be difficult for many British families to accept but insisted that reintegration was vital if peace was to be achieved.
The amnesty extends to all Taliban militants, including those who have taken part in atrocities, such as murdering children, beheadings and hanging women, it said.
The agreement is part of a policy signed by the British Government in which insurgents are being allowed to "walk off the battlefield" and enter a "reintegration" scheme, it said.
The paper said Taliban joining the programme are not interrogated but instead are asked to complete a questionnaire explaining their reasons for joining the insurgency.
More than 2,700 insurgents have been reintegrated into mainstream Afghan society since October 2010, with 800 now described as "showing interest in leaving the Taliban".
Of those, about 90 are from Helmand, where nearly 400 British troops have been killed and more than 5,000 injured.