Staff will work in shifts after a judge ruled the terminally-ill 11-month-old baby would spend the last part of his life in a hospice.
Mr Gard and Ms Yates, who are in their 30s and come from Bedfont, west London, had originally asked Mr Justice Francis to rule that Charlie should be allowed to undergo a therapy trial in NY.
Doctors at Great Ormond Street in London maintained that it was kinder for the Charlie's life support to be switched off. But the hospital "has suggested that he should be removed from life support within hours of being transferred to a hospice".
He said it was three and a half months since his original decision that Charlie be allowed to die with dignity. "However, he said that "(i) t looks like the chances are small" of the boy being brought home.
The hospice's name and the time Charlie will be moved will not be made public, the judge ordered. Charlie was diagnosed with infantile onset encephalomyopathic mitochondrial DNA depletion syndrome, an incurable autosomal recessive disorder that causes a drop in an individual's mitochondrial DNA in affected tissues.
The hospital argued that it had "moved heaven and earth" to fulfill the parents' wishes, but said that no intensive care pediatric doctor in the country was able or willing to supervise his care at home.
But they disagreed over the detail of care plans.
Once there, the baby's life support eventually would be switched off.
It said: "Please only email if you can help us!" The hospital's lawyers demanded that a decision be made today, and have said that Gard should either stay at the hospital or die the same day he is admitted to hospice.
British courts and the European Court of Human Rights sided with the hospital in a string of hearings since March.
Following the hearing, Charlie's godfather James Evers accused GOSH of putting "arduous conditions" in the way of Ms Yates and Mr Gard's wishes.
He issued an order barring publication of the name of the hospice and the date when Charlie is taken there. "We can not know if Charlie would have responded to the experimental therapy".
But they abandoned their legal fight on Monday after concluding that Charlie had deteriorated to the "point of no return". "Unfortunately, a MRI scan of Charlie's muscle tissue conducted in the past week has revealed that it is very unlikely that he would benefit from this treatment".