The first 7,500 teachers were last week due to get 50 per cent subsidies, up to the value of pound;500, towards the cost of a laptop or desktop computer.
The payments were to be counted as part of teachers' salaries by the Inland Revenue and are subject to income tax and NI.
Caroline St John Brooks, TES editor, welcomed the climbdown, by the Department for Education and Employment, which will save teachers up to pound;200.
She said: "This is great news - and shows that The TES's campaign is having an ipact.
"Teachers need to have the tools to do the job - - but it is also crucial for staffroom morale that they feel their efforts are appreciated.
"It is very important that the department does not appear grudging in its financial support, and this decision is a step in the right direction."
A DFEE spokeswoman said: "We have listened to teachers and we want this to be a simple scheme which takes the worry out of buying as laptop. So, if we are going to stick to that principle, we are prepared to pay the tax and national insurance costs.
"This will also mean teachers are not left having to fill in complicated forms to declare the tax which would have been due."