Chris Gard and Connie Yates announced their decision as a High Court judge was preparing to oversee the latest round of a five-month legal battle.
Mr Justice Francis had been scheduled to analyse what the couple said was fresh evidence at a hearing in the Family Division of the High Court in London.
A lawyer representing Charlie's parents told Mr Justice Francis that "time had run out".
"This case is now about time," said their barrister Grant Armstrong, adding: "Sadly time has run out."
Mr Armstrong said Charlie's parents had made a decision following the latest medical reports and scans.
Mr Armstrong said damage to Charlie's muscle and tissue was irreversible.
"The parents' worst fears have been confirmed," he said
"It is now too late to treat Charlie."
The couple felt that continuing their fight would cause Charlie pain, said Mr Armstrong.
He said the case was "worthy of a Greek tragedy".
Mr Armstrong said Charlie's parents hoped to set up a foundation.
He said they wanted lessons to be learned.