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."
Armstrong said Charlie's parents had made a decision following the latest medical reports and scans.
The couple felt that continuing their fight would cause Charlie pain, he said, adding they hope to set up a foundation as part of their son's legacy.
Connie Yates read out a statement to a packed room at the High Court. The couple wept as she said: "So sorry that we couldn't save you."
"This is one of the hardest things that we will ever have to say and we are about to do the hardest thing that we'll ever have to do which is to let our beautiful little Charlie go.
"Put simply, this is about a sweet, gorgeous, innocent little boy who was born with a rare disease, who had a real, genuine chance at life and a family who love him so very dearly and that's why we fought so hard for him.
"We are truly devastated to say that following the most recent MRI scan of Charlie's muscles, as requested in the recent MDT meeting by Dr Hirano; as Charlie's devoted and loving parents we have decided that it's no longer in Charlie's best interests to pursue treatment and we will let our son go and be with the angels."
Roger Kiska from the Christian Legal Centre insists that it may have been a different ending if the courts respected the parents' rights.
"Had they been giving the parental rights that should have belonged to them in the first place it wouldn't have been too late to do the therapy. So for me this is on the system that they should have allowed the family to make their own decision."
He continued: "Pray for the family. As a family this will obviously be an incredible tragedy for them. They've been fighting for a long time and they've had hope and I guess today marks the end of that hope. "
Connie Yates added: "All we wanted to do was take Charlie from one world renowned hospital to another world renowned hospital in the attempt to save his life and to be treated by the world leader in mitochondrial disease.
"We feel that we should have been trusted as parents to do so but we will always know in our hearts that we did the very best for Charlie and I hope that he is proud of us for fighting his corner.
"Charlie had a real chance of getting better. It's now unfortunately too late for him but it's not too late for others with this horrible disease and other diseases. We will continue to help and support families of ill children and try and make Charlie live on in the lives of others. We owe it to him to not let his life be in vain."
Connie Yates also thanked their legal team who fought on their behalf for free. She also thanked their supporters all over the world and also staff at Great Ormond Street Hospital (GOSH) which she said gave him care that was second to none.
"Charlie has had a greater impact on and touched more people in this world in his 11 months than many people do in a life time. We could not have more love and pride for our beautiful boy.
"His body, heart and soul may soon be gone, but his spirit will live on for eternity and he will make a difference to people's lives for years to come."
As news of Charlie Gard's fate broke outside the High Court, a group of "Charlie's Army" supporters burst into tears and started screeching angrily through megaphones.
They severely criticised Great Ormond Street Hospital (GOSH), claiming they had "failed" the infant and "denied" him a life-giving opportunity.
Breaking down and hugging each other, they demanded "justice" and chanted "Shame on GOSH. Shame. Shame. Shame ... Charlie's Army never sleeps."
One visibly distressed woman fell to the ground and shouted: "He had a chance and you took it away." Meanwhile, one girl sang through a megaphone while fighting back tears.
Dorit Ronen said: "I'm shocked, I really don't understand how this could happen. How could they not give him one chance?"
Around 20 supporters of the terminally ill infant had gathered outside the High Court with megaphones, blue balloons and banners.
The group, of mainly women and children, are part of the "Charlie's Army" movement. They chanted slogans and cheered when passing cars beeped their support.
David Gillespie from St Andrews, flew from Scotland on Monday morning to be there. He told the Press Association: "This boy has to have one chance. That's it. He's not had one in life.
"I had one with a heart attack. He's not even had one at anything."
