The boy from Merseyside, who had a degenerative brain condition, died at 02: 30, his father Tom Evans said.
On Facebook he wrote: "My gladiator put down his shield and gained his wings ... absolutely torn apart".
Alfie's parents lost the legal challenge against a Supreme Court ruling that allowed the hospital to turn off artificial ventilation after it had been in a semi-vegetative state for more than a year.
The legal campaign of Mr Evans and Alfie's mother, Kate James, attracted media attention and saw them clash with doctors over the treatment of the baby.
Alfie, born in May 2016, was first admitted to Liverpool's Alder Hey Children's Hospital the following December, after suffering from seizures, and has since been hospitalized.
The parents, who lived in Bootle, wanted to take the child away from the hospital for treatment in Italy, but this was refused by doctors who said continued treatment was "not in Alfie's interest".
The hospital said the scans showed "catastrophic degradation of his brain tissue" and that further treatment was not only "futile" but also "inhumane".
