The forces will be training Iraqi and Kurdish forces fighting militants from the Islamic State (IS) group and are set to be joined by a small "force protection" deployment who will defend them, Fallon added.
"We have not finalised numbers yet -- obviously we have got a lot of kit back from Afghanistan that we can make available -- but we are talking very low hundreds," he told the newspaper.
Britain currently has some 50 personnel in Iraq training Iraqi and Kurdish forces.
Fallon last month signalled an increase in the number of British forces in Iraq but this is the first confirmation of numbers.
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He told the Telegraph that they would be based at four locations -- one in Kurdish territory and three others closer to Baghdad.
They are likely in particular to be training local forces on bomb disposal techniques, sharing expertise gained while fighting in Afghanistan.
Britain is taking part in US-led air strikes aimed at driving IS jihadists out of significant parts of Iraq but is not joining strikes on targets in Syria.
It was one of the main members of the US-led "coalition of the willing" which invaded Iraq in 2003 and overthrew dictator Saddam Hussein.
But Prime Minister David Cameron has ruled out sending combat troops back into Iraq, faced with voters weary of war after 13 years in Afghanistan who go to the polls for a general election in six months.