The 11-month-old's parents told of their pride in their "beautiful little boy" who died from a rare genetic condition on Friday.
The infant was at the centre of a legal battle between his parents and Great Ormond Street Hospital (GOSH) over his care that attracted worldwide attention.
Pope Francis, Prime Minister Theresa May and US vice president Mike Pence were among those to pay tribute to the youngster after Charlie's mother Connie Yates confirmed news of her son's death.
"Our beautiful little boy has gone, we're so proud of him," Ms Yates said in a statement.
Ms Yates and Charlie's father Chris Gard had wanted to take their severely ill son to the US for treatment.
But after the couple accepted he could not be given the experimental therapy, a court ordered on Thursday that he be moved to a hospice where his life support would be withdrawn.
GOSH, where Charlie spent most of his short life, sent "heartfelt condolences" to his family, while Mrs May said she was "deeply saddened" by his death.
"Everyone at Great Ormond Street Hospital sends their heartfelt condolences to Charlie's parents and loved ones at this very sad time," a GOSH spokeswoman said.
Mrs May said: "I am deeply saddened by the death of Charlie Gard. My thoughts and prayers are with Charlie's parents Chris and Connie at this difficult time."
The Pope, who had shown his support for Charlie's parents during their lengthy legal challenge, tweeted: "I entrust little Charlie to the Father and pray for his parents and all those who loved him."
Charlie's plight saw hundreds of supporters - called Charlie's Army - lending their voices and money for him to be given treatment, with £1.35 million raised on an online fund-raising site.
US president Donald Trump also weighed in, saying the United States would be "delighted" to help if it could.
Following news of Charlie's death, Mr Pence tweeted: "Saddened to hear of the passing of Charlie Gard. Karen & I offer our prayers & condolences to his loving parents during this difficult time."
On Thursday Ms Yates claimed she and Charlie's father were "denied" their "final wish" when a High Court judge approved a plan to see Charlie moved to a hospice.
His parents had pleaded to be allowed more time with him, after their earlier request to take him home to die also failed.
Charlie, who was born on August 4 last year, had a form of mitochondrial disease, a condition that causes progressive muscle weakness and brain damage.
Described as "perfectly healthy" when he was born, Charlie was admitted to hospital at eight weeks and his condition progressively deteriorated.
The couple said they wanted to take their son across the Atlantic for nucleoside bypass therapy, but specialists at GOSH in London, where Charlie was being cared for, said the treatment was experimental and would not help.
Earlier this month the Vatican press office said the pontiff prayed that "their wish to accompany and treat their child until the end is not neglected".
The protracted legal battle saw the couple take their case to the High Court, Court of Appeal and Supreme Court - all of which ruled life support treatment should end and Charlie should be allowed to die with dignity.
Judges at the European Court of Human Rights refused to intervene in the case and the couple said they felt "let down" following the series of court hearings.
Paying tribute to their son following the end of their legal challenge on Monday the pair, both in their 30s, of Bedfont, west London, described him as an "absolute warrior".
Mr Gard gave an emotional speech on the steps of the High Court when he said: "Mummy and Daddy love you so much Charlie, we always have and we always will and we are so sorry that we couldn't save you."
At the time Charlie's parents added they believed their son might have been saved if experimental therapy had been tried sooner, and said time had been "wasted".
Doctors at GOSH did not agree, with lawyers representing the hospital saying the "clinical picture" six months ago had shown irreversible damage to Charlie's brain.
They said the "unstoppable effects" of Charlie's rare illness had become plainer as weeks passed.