More than 500,000 copies of the novel written by Geraldine McCaughrean have been published in English but it will also be available in many other languages including Basque, Chinese, French, Hebrew and Polish.
About 200,000 copies have gone on sale in the United States and 50,000 in Britain.
"I'm more nervous now than I was when I signed on because I just didn't realise in my ignorance that it was going to be quite that big," said McCaughrean.
"I thought it was a very English kind of a book, possibly American, but not Korean and Russian. It's just very exciting".
As with the hugely successful Harry Potter series, details of the book were shrouded in secrecy before publication on Thursday.
The sequel is set in 1926, and Michael, one of the children in the original, has been killed in the first world war. Wendy is now a wife and mother but returns to Neverland which is "colder, and more dangerous and more frightening than it was before," McCaughrean said.
Great Ormond Street Children's Hospital, which was given the copyright to Barrie's original story in 1929, is hoping to raise as much money as it can from the sequel before its European rights on the original run out at the end of 2007.
McCaughrean was chosen after the London hospital began a search for a writer in August 2004. Nearly 200 authors from around the world submitted a sample chapter and synopsis before she was picked.
Peter Pan in Scarlet is expected to fly to the top of the bestseller lists, with the British print run largely accounted for by pre-publication orders, according to Oxford University Press, the book's main publisher.
"Now I'm quivering like a greyhound, waiting to see what people think of my book when it finally hits the shops," said McCaughrean, who will share royalties for the novel with Great Ormond Street.
"I am bracing myself against the bad reaction. I've never incited enough interest to get antagonistic reaction to my books, but for the first time I know I will. I know people think I shouldn't do this because I'm not Scottish and not a man."
Great Ormond Street said that McCaughrean had kept the integrity of the original story, whereas other adaptations had tended to play down the darker aspects of Barrie's vision.
David Barrie, great-great-nephew of the author, said: "JM Barrie could never have guessed that Peter Pan would still be making a vital difference to Great Ormond Street Hospital almost 70 years after his death.
"I'm sure he would be delighted to know that, thanks to Geraldine McCaughrean's sequel, the boy who wouldn't grow up will go on helping children back to health for many years to come."