Prime Minister David Cameron had initially decided to discourage the interpreters from settling in Britain for fear of the message it would send out about the stability of Afghanistan as foreign forces pull out.
Many of the Afghans say their lives are in danger from the Taliban due to their work with British forces in the restive southern Helmand Province.
British forces are due to withdraw at the end of 2014 along with other troops in the NATO-led international coalition.
They will reportedly be able to choose between cash payments if they stay in Afghanistan or settle in a country nearby, and the right to move to Britain.
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Those who wish to remain in Afghanistan will be paid their salary for five years if they train or study, or be paid for 18 months if they do not.
"These proposals give them a choice: the opportunity to go on working in Afghanistan, learning new skills and to go on rebuilding their country or to come and make a new start in Britain," a source in Cameron's Downing Street office said.
One of the Afghan interpreters, who wished to be identified only as Mohammad, said London had made "the right decision".
"Saving those people who have helped the British government is giving a message to the Taliban that the Afghan interpreters will not be left behind for them to be persecuted and hunted down by the terrorists," he told AFP.
Mohammad was forced to leave his wife and three children behind in Afghanistan after receiving death threats from the Taliban for his five years' work with British troops.