The Berkshire-born soldier was killed by small arms fire in the al-Ashar area of Iraq's second city while escorting a police training team.
The Ministry of Defence (MoD) said that the teenage soldier was shot by an "opportunistic" gunman while checking part of the patrol's route on foot.
He was taken immediately to Basra Palace but died from his injuries.
Rifleman Donnachie's company commander Major Alex Baring described the 18-year-old as the "best of British".
"Rifleman Donnachie, or Donny as he was known to his mates, was the epitome of what it is to be professional. Born and bred in Reading, the army was his life. He only arrived from training in December as a Royal Gloucestershire Berkshire and Wiltshire Light Infantry recruit."
Major Baring added that the soldier was "no average rifleman" and, "despite having been involved at the front end of strike operations and numerous contacts against the enemy in Basra City, he had already volunteered to deploy to Afghanistan later this year".
Lieutenant Colonel Justin Maciejewski, commanding officer of Second Battalion the Rifles, said that his regiment was "grieving the loss of a superb soldier who wanted to make a difference, and put himself in harms way to make Basra a better place for Iraqis".
"He paid the ultimate sacrifice by laying down his life while protecting other members of his patrol. He loved his work and took great pride in it. We are so very proud of him and honoured to count him as one of our comrades," Lt Col Maciejewski continued.
"None of us here will ever forget him. He had such energy and humour. Our thoughts and our prayers are very much with Paul's family at this time of terrible and overwhelming grief."
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