Alfie's father Tom Evans announced the news on his social media, saying: "My gladiator lay down his shield and gained his wings. absolutely heartbroken".
Purple and blue balloons scattered across the cloudy sky of Liverpool on Saturday as people chanted "Alfie, Alfie, AlfIe". Trump has not mentioned Alfie's case.
Doctors overseeing his care said further treatment was futile and he should be allowed to die.
One family member said Tom was "blowing and blowing and blowing" but despite his efforts, the 23-month-old tragically passed away in his parents' arms. If an agreement can not be reached between the parents and doctors, "a court should be asked to make a declaration about whether the provision of life-sustaining treatment would benefit the child".
Pope Francis had intervened in the case that has attracted worldwide attention, writing on Twitter that he hoped the parents' "desire to seek new forms of treatment may be granted".
The death of Alfie, who had a rare degenerative brain condition that left him in a "semi-vegetative state" with nearly no brain function, came five days after doctors removed life support. Alfie was even granted Italian citizenship to travel.
"Goodbye, little Alfie. We loved you", Italian Foreign Minister Angelino Alfano tweeted Saturday.
A "sick and psychotic" minority of supporters saw the hospital put on lockdown two days later after threats were made to burn down the hospital and rumors swirled about a planned raid.
There have also been concerns about the actions of supporters in other high-profile life-support cases, including the cases of Charlie Gard and Isaiah Haastrup, who both died in the past year amid acrimonious legal battles between their parents and doctors.
Gemma said: "So sad to hear about the lovely Alfie Evans".
Speaking for the first time since burying Charlie they offered Alfie's parents hope as they come to terms with their grief.
Alder Hey issued a statement to express "heartfelt sympathy and condolences to Alfie's family". He talked about his sadness and he talked about Alfie being embraced by the Lord in heaven. "This has been a devastating journey for them, and we would ask that their privacy and the privacy of staff at Alder Hey is respected".
Alfie's case has drawn worldwide attention, with officials in largely Catholic Poland and Italy implicitly criticizing Britain's courts and state-run National Health Service.
Thousands of people from all over the world got behind the parents of Alfie Evans in the desperate battle to keep their toddler alive. The answer ties into wider questions - about medical ethics and what it means for a life to be "not worth living", and about popular trust, or lack thereof, in the UK's National Health Service, a paradigmatic example of both the pros and cons of socialized medicine. A leading right-wing politician in Italy, Veneto Gov. Luca Zaia, said that in Alfie, the "so-called civilized world has supplied the latest proof of enormous incivility". At one point, dozens tried to storm the hospital's front entrance.
"Alfie is doing still as well as he can".