His parents were among those who died, but he says he is looking forward to hugging his sisters with his new arms.
He was fitted with them at Queen Mary's Hospital in south-west London, the Daily Mirror newspaper reports.
One of them is a state-of-the-art limb, with a hand that Ali can open and close. It's also got a Man United tattoo!
"My arms feel good. I didn't think they'd look this good," he told the newspaper.
"Now I want to hug my sisters and the rest of my family. I also want to brush my teeth by myself and wash my face."
Ali was airlifted out of Baghdad after coming down with an infection.
He was first taken to Kuwait, then flew on to Britain in August.