He was taken to a field hospital but died from his injuries.
Major Bateson, from Chislehurst, Kent, has been in Iraq for the last three months working on communication links between deployed British forces and the UK.
He competed for the army in the triathlon and orienteering competitions and has been described as "one of life's real characters" by his superiors.
Lieutenant Colonel David Craft, his commanding officer, said: "[Major Bateson's] personality was bigger than simply the job he was doing.
"He was always the person with a smile on his face and a quick retort; the sort of person you need around to lift the team when things don't go well. Nick had a zest and energy second to none."
The fallen soldier's room-mate, Major Tarquin Shipley, added: "Knowing Nick was an absolute privilege.
"He had helped recruit me, was my course officer as a young officer and lately we had studied for a master's degree at Blandford together and shared a room in Iraq. He was incredibly helpful and would not think twice about putting himself out for you."
Major Bateson, who is survived by his wife Angela, is the 147th British fatality in Iraq since the US-led invasion in March 2003.
Defence secretary Des Browne said his thoughts would be with Major Bateson's family and friends.
"We will be providing them with all the support we can at this difficult time," he said.
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