Simone Mastrelli, 30, pleaded guilty at Preston Crown Court to the assault outside Anfield.
It occured before Liverpool played Roma in the Champions League last year.
Mastrelli, from Rome, had been extradited last month after being arrested on a European Arrest Warrant in Italy in connection with the attack on father-of-three Mr Cox, from Dunboyne in Co Meath, Ireland.
Mr Cox suffered serious catastrophic head injuries in the attack, and has been recovering at the National Rehabilitation Hospital in Dun Laoghaire.
He spent four-and-a-half weeks at the Walton Centre in Liverpool, a specialist neurological unit for brain injuries, following the attack on April 24, before being airlifted to another specialist unit at Dublin’s Beaumont Hospital.
Mastrell entered a guilty plea to unlawfully and maliciously inflicting grievous bodily harm on Mr Cox.
He pleaded not guilty to a separate count of violent disorder, also on April 24, which will lie on file after the Crown accepted the plea.
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