According to the report the additional troops will not be taking part in combat operations against the Taliban militants.
UK troops had been due to leave Afghanistan this year but will now have their mission extended into 2017.
The decision is expected to be announced by Prime Minister David Cameron today at a NATO Summit in Warsaw.
British decides to deploy more troops to Afghanistan after U.S. President Barack Obama earlier this week said he will keep more troops in Afghanistan than planned.
In addition, Britain is to extend its £70m a year funding for the Afghan security forces to 2020, committing an extra £178m to the Afghan government of president Ashraf Ghani.
The NATO Summit held in Poland on 8th and 9th of July is expected to approve support and financial funding for Afghan security forces for a period of five years.