The 450-page novel, which is about a war veteran turned private investigator called Cormoran Strike, was acclaimed by critics but Rowling's involvement only came to light after the Times started digging into Galbraith's background.
The paper wanted to know how an author "with a background in the army and the civilian security industry" could write such a strong first novel.
"I had hoped to keep this secret a little longer because being Robert Galbraith has been such a liberating experience," Rowling said.
"It has been wonderful to publish without hype or expectation, and pure pleasure to get feedback under a different name."
According to the Times, The Cuckoo's Calling has sold 1500 copies in hardback so far.
The book was published by Sphere, part of Little, Brown, which published her last novel, The Casual Vacancy.