Archie Battersbee's life support was due to be withdrawn at 10am today, his family had been told.
Speaking to Sky News last night, the 12-year-old's mother Hollie Dance said the hospital "have made it very clear that we've got no more options".
All legal routes have now been exhausted, and she added: "I've done everything that I've promised my little boy I'd do."
Archie has been on life-support since he was found unconscious in April. He was found by his mother with a ligature around his neck, and she has said he was taking part in an online challenge that went wrong.
Doctors who have treated the boy for the past four months say he is "brain stem dead", and he is being kept alive by a combination of medical interventions including ventilation and drug treatment at the Royal London Hospital.
His parents had fought a long-running legal battle over the withdrawal of this treatment - and yesterday, they were dealt a double blow in their last-ditch attempt to have him moved to a hospice.
The family had applied to the Court of Appeal, challenging a ruling that blocked these plans.
The Court of Appeal confirmed shortly after 6.30pm last night that permission to appeal had been refused.
The family then applied to the European Court of Human Rights over the decision, but the court said it would not intervene.
A spokesman with campaign group Christian Concern, which has supported their case, said: "The family are devastated and are spending precious time with Archie."
'Major and unpredictable' risks with hospice move
Archie's mother, Hollie Dance, had said she wanted her son to "spend his last moments" together with family privately, but the High Court ruled the move was not in Archie's best interests, calling the risks "major and unpredictable".
"I understand why some people get to a point where they think enough is enough... but I think where there is hope, there is life, and I do see that with Archie," she told Sky News.
"I still in my heart and in my gut believe that Archie can pull through this."
His parents said they recognised the risks in relation to the transfer - with medical staff warning it could see Archie die on the way to the hospice - but they told the court they were prepared to take these risks rather than remain in hospital.
Initially, the family had been battling for his life support treatment to continue in the hope he would recover.
"As a parent, I want to know that I have done everything in my power to make sure that I tried my hardest for my little boy," Ms Dance said.
Speaking about the court's ruling, she said: "I wouldn't say I have accepted the decision, I don't think I'll ever accept it.
"It's been really hard. Despite the hard, strong face and appearance in front of the cameras, up until now, I've been pretty broken."