The 20-year-old, who had been providing covering fire from his Warrior armoured vehicle, was injured in the incident and died at the scene of the attack.
He is the 145th British soldier to die in Iraq since military operations began more than four years ago.
The Liverpool-born soldier has been described as a "popular, dependable" member of the Duke of Lancaster's Regiment reconnaissance patrol.
"I knew Kingsman Jones to be a soldier with an appetite for soldiering at the sharp end," said Captain Mike Peel.
"An honest, experienced and robust character, he was always willing to assist others in whatever way he could. He will be sorely missed by all who had the honour to serve alongside him."
Kingsman Jones' commanding officer Lieutenant Colonel Mark Kenyon said that he will be remembered as a "very professional soldier who was loyal to his regiment and his friends".
"Above all he was a cheerful and likeable young man who always had time to help others. He was the epitome of all a kingsman should be. Our thoughts and prayers are very much with his family at this time."
Defence secretary Des Browne added: "I was very sorry to hear about the loss of Kingsman Alan Jones. By all accounts he was a popular, dependable young man.
"His family, friends and fellow soldiers in the Duke of Lancaster's Regiment are in my thoughts at this difficult time and I know he will be sorely missed."
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