"Thankyou everyone for all your support", Thomas Evans and Kate James said.
Today, Pope Francis wrote that he is deeply saddened by the death of little Alfie. The Liverpool physicians who worked on his case said the further treatment was futile and he should be allowed to die.
Alfie had been in a coma for over a year and needed a ventilator to keep him breathing but his parents have fought to stop his life support being switched off.
The case drew worldwide support including from Pope Francis, who asked that "their desire to seek new forms of treatment may be granted".
After a series of court cases, doctors at Alder Hey Children's Hospital in Liverpool removed his life support on Monday, April 23, against his parents' wishes.
His parents, Tom Evans, 21 and Kate James, 20, had fought to take their son to a foreign hospital for treatment for a degenerative medical condition, but lost a final court appeal on Wednesday.
"My gladiator lay down his shield and gained his wings at 02:30", his father, Thomas Evans wrote on Facebook.
Mr Evans said their lives had been "turned upside down" by the "intense focus" his case had received.
Members of the Italian association Comitato Articolo 26 take part in the Novena vigil prayer, praying for terminally ill British boy Alfie Evans, at the St Peter's square in Vatican.More news: Spider-Man Will Include Avengers: Infinity War's Slick Iron Spider Costume
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Speaking outside Alder Hey Hospital, Tom said: "We got rejected yesterday to go to Italy unfortunately".
The incident itself has caused incredible amounts of public outrage and campaigning for better treatment, with the hospital staff reportedly shocked after countless acts of abuse towards them.
Alfie Evans died on Saturday morning. 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". In such cases, the rights of the child take primacy over the parents' right to decide what's best for their offspring.
Alder Hey Children's hospital, where the 23-month-old was being treated, expressed their condolences.
It asked those wishing to leave tributes to Alfie to place them at the nearby Springfield Park. Alfie's death comes after a massive legal battle between the hospital and his parents Tom and Kate.
'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 sparked a medical ethics debate that resonated far beyond Britain. Italy even granted Alfie citizenship and put a military plane on standby to transport him to Rome if the courts allowed it.
Support for the toddler grew by the minute all over the globe.