Connie Yates and Chris Gard came to the decision after receiving the results of Charlie's latest brain scans.
Charlie Gard's parents end legal fight to take him to US
The parents of critically-ill British child Charlie Gard have ended their legal fight to take him to the United States for experimental treatment.
Grant Armstrong, the lawyer representing Connie Yates and Chris Gard, told the judge Nicholas Francis that "time had run out" for the 11-month-old.
"For Charlie it is too late. The damage has been done," Mr Armstrong said.
Speaking outside the High Court, Mr Gard described his son as a "warrior" and said he did not believe he would make his first birthday in two weeks time.
Charlie's mother told the court that they had fought to give their baby a chance at life.
She added: "A whole lot of time has been wasted. We are sorry we could not save you."
Mr Gard and Ms Yates made the decision after US neurologist Dr Michio Hirano said he was no longer willing to offer their son experimental treatment, having examined Charlie's latest brain scans.
Judge Francis had scheduled a two-day hearing to consider fresh evidence by Dr Hirano who had come to London from Columbia Medical Center in New York to examine Charlie.
However, Armstrong said that due to delay the "window of opportunity" to treat the child had been lost.
Charlie, who is being cared for at Great Ormond Street Hospital (GOSH), suffers from a rare genetic condition that has left him with brain damage and unable to breathe unaided.
In a case which caught the attention of the world, Mr Gard and Ms Yates had hoped to take their son to the US where he would be given nucleoside therapy. Both US President Donald Trump and the Pope had offered to intervene to help Charlie receive the treatment.
Doctors at Great Ormond Street Hospital said that Charlie should be taken off life support, which was only prolonging his suffering.
The lawyer representing the hospital, Katie Gollop said: “The hearts of each person working at Great Ormond Street hospital and the hearts of the hospital go out to Charlie and his mother and his father .... We have more sorrow than I have words to say.”
While Judge Francis paid tribute to Ms Yates and Mr Gard for the love and care they had given to their son.
Mr Armstrong said that the couple would now look to establish a foundation to help children like Charlie, who was born in August last year.
He said: "The parents wish to treasure their remaining time with Charlie, however short that may be.”