“Our baby grew his wings tonight at 2:30am (0130 GMT). We are heartbroken. Thank you everyone for all your support,” Kate James and Thomas Evans said in a statement on Facebook.
The parents had fought to take their son, who had a degenerative medical condition, from a hospital in Liverpool in northwest England to a clinic in Rome but lost a final court appeal on Wednesday.
Doctors had already removed life support on Monday after the parents lost a previous appeal to keep him alive despite doctors’ recommendations.
Pope Francis intervened several times in a case that attracted worldwide attention, particularly in Italy and Poland.
Earlier this week the pontiff wrote on Twitter that he hoped the parents’ “desire to seek new forms of treatment may be granted”.
Tom Evans had met the pope in the Vatican and asked him to “save our son”.
Italy had also granted citizenship to the toddler in the hope of facilitating his transfer to the Bamino Gesu (Baby Jesus) paediatric hospital in Rome.
The case is the latest in a series of high-profile battles between parents of ill children and the British authorities.
British law states that parents “cannot demand a particular treatment to be continued where the burdens of the treatment clearly outweigh the benefits for the child”.
If agreement cannot be reached between the parents and the healthcare professionals, “a court should be asked to make a declaration about whether the provision of life-sustaining treatment would benefit the child”.
The most recent example was that of Charlie Gard, who was born in August 2016 with a rare form of mitochondrial disease.
He died last year, one week short of his first birthday, after doctors withdrew life support treatment.
Gard’s parents fought a five-month legal battle for him to be taken to the United States for experimental treatment.
The parents of Ashya King defied professionals in 2014 when they snatched their cancer-stricken son from a British hospital and took him to Prague for proton beam therapy.
King, now eight years old, has since been declared clear of the disease.