Chris Gard and Connie Yates have announced that they are ending their legal battle.
The parents said they made the decision following the latest round of medical reports and scans on the boy who was born in August 2016.
"We've chose to let our son go. he's not braindead but a whole lot of time has been wasted".
Armstrong said recent tests showed that Charlie now had irreparable muscular damage, leaving no chance for an experimental treatment the family had hoped to seek in the United States to succeed. "Due to delay, that window of opportunity has been lost".
According to Mr Armstrong the United States neurologist Dr Michio Hirano who was willing to give Charlie treatment had refused after he saw results of a new MRI scan last week.
'This case is now about time, ' said their barrister Grant Armstrong, adding: 'Sadly time has run out'. "It is hoped that those who, like the professor, have provided the opinions that have so sustained Charlie's parents, their hopes and thus this protracted litigation with its many consequences, will also find much upon which to reflect".
A leading legal expert has offered some harsh criticism of the American medical expert at the centre of the Charlie Gard case.
Great Ormond Street Hospital (GOSH) said "the agony, desolation and bravery" of their decision "command GOSH's utmost respect and humble all who work there".
The 11-month-old has is under the hospital's care, whose doctors advised against continuing life support as the child can not move his arms and legs, or breathe without help.
"If Charlie receives this treatment and it does work it won't just be his life that's saved, it will be many more children in future who are born with this terrible disease".
While Judge Francis paid tribute to Ms Yates and Mr Gard for the love and care they had given to their son.
Meanwhile, the couple said they were "extremely upset" at "hurtful comments" they had received from the public.
Gard said, "Without the excellent care of the doctors at GOSH [Great Ormond Street Hospital] our son would not even be alive and not a day goes by when we don't remember that".
Supporters of critically ill baby Charlie Gard and his parents shout slogans during a demonstration outside the High Court in central London on Monday.
Yates and Gard have been fighting successive rulings saying their son's life support should be withdrawn and he should be left to die with dignity.