The figures, released by publisher Penguin Random House, include both print and e-books.
Many bookshops around the country stayed open all night to cope with demand when the novel went on sale on Tuesday.
The book is set 20 years after the events of Lee's 1960 Pulitzer Prize-winning novel To Kill a Mockingbird.
"It's so fabulous to see a book dominating the news agenda and to be reminded of just how important literature and reading is to all of us," said publisher Susan Sandon.
"I speak for everyone at Penguin Random House when I say how privileged we are to be part of this piece of publishing history."
The novel has had mixed reviews, with many Harper Lee fans shocked to discover that Atticus Finch, the moral centre of To Kill a Mockingbird, is painted as a racist "bigot".
Lee wrote Go Set a Watchman in the mid-1950s - but her editor persuaded her to turn some of the story's flashback sequences into a separate novel.
That novel became To Kill A Mockingbird, which went on to be regarded as one of the greatest novels of the 20th Century.
Penguin Random House wouldn't comment on how Watchman's first-day sales compared to EL James' Fifty Shades spin-off novel, Grey, which was published in June.
It said last month that Grey had broken the first week UK sales record for adult books, selling 647,401 copies in its first three days, beating record holder Dan Brown's The Lost Symbol, which sold 551,000 copies in five days in 2009.
The new novel by Harper Lee, Go Set a Watchman, sold more than 105,000 copies in the UK on its first day.