He is one of a growing number of New Zealand crime authors, including Vanda Symon, Paddy Richardson, Paul Thomas and Chad Taylor, who have sold books overseas, particularly in the crime fiction-hungry German market.
Cleave's success, though, puts him in a class of his own. He is a bestseller in Europe, has a top UK-based literary agent and his work has been translated into 14 languages.
His seventh and latest novel, Joe Victim, went on sale in New Zealand on Friday just before a US release. It's a sequel to his first book, The Cleaner, which has been a huge hit offshore. It sold about 200,000 copies in France and 300,000 in Germany, and became one of New Zealand's most successful novels overseas.
Previous books, which include Blood Men, Collecting Cooper and, most recently, The Laughterhouse, are stand-alone stories but share a Christchurch setting and interlinked characters, including ex-cop turned private detective, Theo Tate.
Blood Men reached the top spot on Amazon in the US and the film rights to The Cleaner have been sold to noted French producer Pierre-Ange Le Pogam, who worked on the Liam Neeson film Taken. Cleave hopes it will make it to the big screen.
He is not in the same league as Michael Connelly or Lee Child but it's not a bad track record for a guy who left Christchurch's Papanui High School at the start of his seventh-form year. He spent several years working in a pawn shop - where he gained insights into the city's darker side - and, inspired by Stephen King, started writing horror stories as a 19-year-old.
His commitment to his goal extended to selling his house and moving in with his parents so he could keep working on his first novel, and it finally paid off when he became a published author at 31.
Before his first deal with Random House was signed, Cleave was ready to give up on his long-held dream of becoming a writer.
"Some of my friends believed it was going to happen," he recalls, "but when you get rejection after rejection, you start to think it's not going to work."
Now he counts some of his crime-writing idols - John Connolly, Mark Billingham, R.J. Ellory - as friends and travels the world attending book fairs and festivals. He spends half the year in London, where his 18-month-old son Leo lives, and the rest in Christchurch.
His troubled characters complain about the city in his books but Cleave loves the place. "I've always lived here. It's a cool city."
Joe Victim marks the return of Cleave's memorable protagonist Joe Middleton, a malignant mixture of rapist, cat murderer, and serial killer known as the 'Christchurch Carver'. In Joe Victim, he's in jail awaiting trial and planning to use the insanity defence to walk free. Early in the book he gleefully imagines knifing an unconvinced psychiatrist; meanwhile, a referendum is about to be held on whether New Zealand should bring back the death penalty.
Cleave writes his nastier characters from a first-person perspective and says it's a deliberate ploy to put his readers inside their heads and see their warped view of the world. The aim is to make it more conflicting when they find themselves relating to someone so creepy.
"All my nasty people, all the serial killers, are the way they are for a reason," he says. "I always try to make it that if you went through the same situations that you might make the same decisions."
He admits that when he's writing about Joe who, despite being a psychopath, shares his black sense of humour, "there's a lot of laughs".
He has something else in common with his character: they were both picked on in high school, and Cleave says with some bitterness that he "forgives no one" for the way he was treated back then.
Cleave's reputation is for dark, disturbing thrillers but he doesn't think his writing is too explicit.
"A lot of people read the books and say, 'That was really violent and really gory' but I think it's more the way they perceive them. All the gory things happen to the bad people."
But it's clear he takes satisfaction from rattling readers. When his early attempts at horror-writing didn't work out, he decided crime novels were scarier because the violence in them could happen in real life.
"If you read a vampire novel, you're not going to come home and check the back door to make sure it's locked in case there's a vampire out there, but if you read a really creepy serial-killer novel, you might be checking the door. That's real-life horror."
Christchurch has gone through massive change since Cleave began using it as the setting for his novels, and the huge effect of the earthquakes has presented him with a dilemma. Readers and reviewers have questioned why the Christchurch in his books is unchanged by the real disaster and the damage, demolition and rebuilding that has followed.
Cleave feels that using the earthquake as a plot device would be hugely insensitive, despite helpful suggestions from some fans that he should write about a murder victim being found in the rubble.
In a prologue to Joe Victim, he says the Christchurch of his books is not the real Christchurch, and his books are about giving readers an entertaining ride.
"I'm not going to use the earthquake to entertain people."
He's not ruling out introducing some post-quake elements in a later novel if he can manage to do it in a credible way. "But it's a decision that I get to make, not other people."
Craig Sisterson, founder of the Ngaio Marsh Award for best crime novel, which Cleave won in 2011 for Blood Men, reckons Cleave is New Zealand's leading contemporary crime writer in terms of overseas sales and success.
It would be great, he says, if Cleave could do for New Zealand what Ian Rankin and Val McDermid have done for Scotland's reputation, and Henning Mankell and Stieg Larsson have done for Sweden's.
"He could become the author who persuades a wide readership to consider the other quality crime authors also producing great work from our country."
Penguin publishing boss Debra Millar says Cleave is in "another stratosphere" to other Kiwi crime writers.
"You can add another zero on to the end of his sales figures internationally."
She attended last year's Frankfurt Book Fair where Cleave spoke on a panel, and says he was treated like a superstar. "There were fans travelling across the country to come and meet him. He's got a huge following in Germany.
"He is a really well-recognised name and his popularity is also growing rapidly in France and in the United States."
She is confident his international success will soon be repeated here.
Cleave would, of course, love his books to sell 50,000 copies here instead of just a few thousand: "Out of the all the countries where I get published, New Zealand is the most important to me emotionally, and I always want to do well here. So I'm hoping it will happen with this book. I think people are going to like it."
