The Cuckoo's Calling, her first book written under the pen name Robert Galbraith, was published last April and had sold fewer than 1,000 copies before The Sunday Times unmasked Rowling to be its author.
It has gone on to sell more than 600,000 English language copies in hardback and another 1 million in eBook form.
The Silkworm, the second in the series, was written before the first was published and will be released in June.
Rowling, 48, has mapped out a series of up to seven crime novels featuring her private investigator Cormoran Strike, the report said.
In The Silkworm, Strike, a war veteran who lost a leg in Afghanistan before becoming a private investigator, will probe the disappearance of a novelist called Owen Quine, who has been writing poisonous-pen portraits of people he knows.
Friends of Rowling say she has found her feet with the crime genre after the success of the Potter books, which sold more than 450 million copies, spawning eight films and even a theme park in Florida.
While The Cuckoo's Calling, which vividly depicts a louche Mayfair demi-monde, was well received by critics, The Casual Vacancy, her first adult novel published in 2012, drew a mixed response.
Despite that, the book, which is set in a fictional West country village, is to be turned into a three-part BBC series later this year.
In 2006, Rowling said her decision to sketch out the entire Potter series had been "lambasted" by some.
She said: "I think they thought it was very arrogant of me to write the end of my seven-book series when I did not have a publisher and no one had heard of me.
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