The decision was announced on Friday by Supreme Court president Lady Hale, Lord Kerr and Lord Wilson.
Alfie's parents had relied on a habeas corpus bid to get the court to agree with them that they have the right to withdraw Alfie from the hospital since they are his parents and legal guardians. Doctors at Alder Hey have said life-support treatment should stop because further treatment was futile.
The parents of a seriously ill baby who want to take him to Italy for treatment have lost the latest round of their legal fight after the UK's highest court ruled that nearly all of their son's brain had been destroyed.
He noted, however, that "Alfie is a British citizen and Italy respects the decisions made in the framework of British national jurisdiction" and that "the British national healthcare system and medical standards are among the highest in the world".
Evans, 21, and his partner Kate James, 20, have fought an ongoing legal battle to allow them to take Alfie overseas for treatment.
"There is also no reason for further delay".
Giving reasons for the decision, the justices said it was a "desperately sad case". That is the law in this country.
"We have instructed our lawyers to submit an urgent application to the European Court of Human Rights, and they have done so today".
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Alfie's parents had previously lost one round of fights, in the high court, court of appeal, supreme court and the European court of human rights.
Mr Evans met with Pope Francis in the Vatican on Wednesday (April 18), pleading with him to "save our son" in a Facebook post after.
"Alfie looks like a normal baby", they said, "but the unanimous decision of doctors who have examined him and the scans of his brain is that nearly all of his brain is destroyed". The protests at the hospital lasted for five days, until Tom and Kate asked supporters to disperse.
Alfie, born on May 9 2016, is in a "semi-vegetative state" and has a degenerative neurological condition doctors had not definitively diagnosed. The condition has eaten away at his brain matter.
The pope had already spoken about Alfie earlier this month. Were the Bambino Gesu staff to treat Alfie, they would have given him a tracheotomy and fed him through his stomach in order to make him more comfortable.
Having reviewed the application the Supreme Court concluded that "The release to which (Alfie) is entitled, therefore, is release from the imposition of treatment which is not in his best interests".
The court refused to release details about the approved plans for Alfie's eventual death, citing Alfie's privacy.