Many bookshops remained open all night to cope with demand. Several hundred snapped up copies at midnight at Foyles bookstore in London.
The book is set 20 years after the events of Lee’s 1960 Pulitzer Prize-winning novel To Kill a Mockingbird.
“We had a buzzy evening with the queue starting to form at 10pm,” said marketing manager Simon Heafield.
“If this evening is anything to go by, Go Set a Watchman will live up to its billing as the publishing event of the year.”
In Harper Lee’s hometown, Monroeville in Alabama, a delivery of 7,000 copies of Go Set a Watchman arrived at the small independent Ol’ Curiosities and Book Shoppe shortly before midnight.
“I’ve had people calling from as far away as from England looking for the book early,” shop keeper Spencer Madrie told Reuters news agency. There were cheers when the shop’s doors opened.
Watchman contains some of the same characters at Mockingbird, including Scout and her father Atticus Finch. It has already proved controversial as early reviewers noted that Atticus expresses racist views in the story.
The story opens with Scout, now 26 and known as Jean Louise, returning on a train to her Alabama hometown from New York.
Tracy Chevalier, author of the bestselling novel Girl With a Pearl Earring, told BBC Radio 4’s Today programme that Watchman was a “roller coaster” of a read.
“It’s making literary history to have a book that has a different take on characters that we’ve all grown to love,” she said.
“I tried to read it simply on its own… There’s some great storytelling in it.”
Publicity-shy author Lee, who is now 89 and lives in a nursing home in Monroeville, originally wrote the book in 1957, before reworking it with her editor to become courtroom drama To Kill a Mockingbird.
The story of racism and injustice in the fictional town of Maycomb in the American South went on to sell 40 million copies and be studied in schools around the world.
Mockingbird was also made into an Oscar-winning film starring Gregory Peck as lawyer Finch, who defends an innocent black man accused of raping a white woman.
The existence of Go Set a Watchman was revealed in February and it is being released in 70 countries simultaneously.