The Christian parents of twelve-month-old Isaiah Haastrup (pictured above with an auntie) had fought against an application by King's College Hospital in London to move him to palliative care.
The couple's "last resort" appeal to the European Court of Human Rights (ECHR) in Strasbourg, France, was dismissed on Tuesday.
Isaiah died at 7.50pm on Wednesday, hours after being removed from life-support, father Lanre Haastrup said on Facebook.
Mr Haastrup and Takesha Thomas, Isaiah's mother, asked the ECHR to intervene after losing two legal battles in England.
A High Court judge had given doctors permission to provide only palliative care to Isaiah against the wishes of Mr Haastrup and Miss Thomas.
Mr Justice MacDonald analysed evidence at hearings in the Family Division of the High Court in January.
Specialists at King's College Hospital in London had said providing further intensive care treatment was futile and not in Isaiah's best interests.
Mr Haastrup and Miss Thomas, who are both in their 30s and from Peckham, south-east London, subsequently failed to persuade Court of Appeal judges to overturn Mr Justice MacDonald's decision.
They then made a written application to the ECHR as a "last resort", which was declared "inadmissible".
Mr Haastrup said on Wednesday that judges had not listened to their arguments.
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