The boy from Merseyside, who had a degenerative brain condition, died at 02:30 BST, his father Tom Evans said.
On Facebook he wrote: "My gladiator lay down his shield and gained his wings... absolutely heartbroken."
Alfie's parents lost all legal challenges to a court ruling allowing the hospital to withdraw ventilation.
The boy had his life support withdrawn on Monday after being in a semi-vegetative state for more than a year.
The legal campaign, launched by Mr Evans and Alfie's mother Kate James, attracted widespread attention and saw them clash with doctors over the child's treatment.
The case drew international support including from Pope Francis, who asked that "their desire to seek new forms of treatment may be granted".
Earlier in April, Mr Evans pleaded with him to "save our son" during a meeting in Rome.
A statement from Alder Hey Children's Hospital in Liverpool, where Alfie was treated, said staff expressed their "heartfelt sympathy".
"All of us feel deeply for Alfie, Kate, Tom and his whole family and our thoughts are with them. This has been a devastating journey for them," it said.
It asked those wishing to leave tributes to Alfie to place them at the nearby Springfield Park.
Supporters of Alfie's parents, known as Alfie's Army, said balloons would be released at the park at about 14.30 BST and asked for attendees to remain "peaceful and respectful".
The RC Archbishop of Liverpool, Malcolm McMahon, said: "All who have been touched by the story of this little boy's heroic struggle for life will feel this loss deeply.
"Now it is time for us to give Tom and Kate space to grieve their son's death and offer our prayers for him and consolation for all."
Everton FC tweeted: "Everybody at the Club is deeply saddened by the loss of the brave young Evertonian. Our thoughts and prayers are with his family."
The Bradley Lowery Foundation, named after the six-year-old boy who died after suffering from neuroblastoma, paid tribute to Alfie's parents, saying "they did everything they could for their little boy".
Alfie, who was born in May 2016, was first admitted to the hospital the following December after suffering seizures, and had been a patient ever since.
His parents, who live in Bootle, wanted to fly the toddler to an Italian hospital, but this was rejected by doctors who said continuing treatment was "not in Alfie's best interests".
Alder Hey Hospital said scans showed "catastrophic degradation of his brain tissue" and that further treatment was not only "futile" but also "unkind and inhumane".
The couple heavily criticised medical staff, with Mr Evans suggesting his son was a "prisoner" at the hospital and had been misdiagnosed.
Hospital bosses were backed by the High Court, which ruled in their favour on 20 February, after accepting medical evidence that there was "no hope" for the youngster.
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