Recruitment officers have attributed the rise to its high-profile advertising campaigns, including a recent drive for infantry recruits and another for the Everest West Ridge campaign.
The Everest campaign, created by Publicis, has helped deliver a quarter of the year's 40,000 target enquiries in just eight weeks.
The TV, radio, press and posters launched in April, and were based on an attempt by British soldiers to reach the summit of Everest by the most dangerous route.
Defence Minister Adam Ingram, in a speech to be made to Harrogate Army Foundation College graduating students today, will say: "I am pleased to say that this year we have seen a significant increase in those expressing an interest in joining the Army, where you have led, others follow.
"Public support for our forces is vitally important. It is justifiably very high. Eighty per cent of the British public thinks our army is among the best in the world."
Despite the Royal Engineers, Royal Armoured Corps, Royal Signals and Royal Electrical and Mechanical Engineers units all exceeding annual recruitment targets, the Army has still fallen short of its overall target by more than 1,000 soldiers.
The news comes as the Army deals with a tough recruitment market, not helped by negative publicity over deployments in Iraq and Afghanistan, as well competition from other employers, low unemployment and further education reducing the number of potential recruits.
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