When it comes to concern for the wellbeing of the well-known, Keanu Reeves is in a class of his own. Last year, all it took was a picture of the 46-year-old sitting alone on a bench, morosely contemplating a sandwich, to go viral – and suddenly a global Cheer Up Keanu Day had been mobilised (15 June, in case you missed it). Nobody knows quite how this happened, but somehow it could only happen to Reeves. Maybe it's his serene-to-the-point-of-stoned screen persona; but it's also, perhaps, the knowledge that Reeves has known, and transcended, genuine suffering in the course of his life – absent parents, deaths of loved ones, and so forth.

So what does it mean now the actor has written his first book and called it Ode to Happiness? "I draw a hot sorrow bath," reads the first page. "In my despair room," reads the second. Each page wallows in increasingly absurd levels of self-pity, while the accompanying blotchy, black-ink drawings, by Los Angeles artist Alexandra Grant, look as if they've been blurred by tears. It culminates with an image of a bleeding black spot and the line: "It can always be worse." Before the UN intervenes with a Cheer Up Keanu relief effort, it should be noted that Reeves's slender literary debut is not entirely serious.

Nor is Reeves himself, as he explains the genesis of his book: "I was in my kitchen hanging out with my friend Janey, and the radio was on – and this station was playing, like, an orgy of depressing, self-pitying, nostalgic music. You know: 'I'm so lonely and I've been left and my heart is broken.' It was so voluptuously horrible. And I just started to write on this piece of paper, because I had this image of, you know, that moment when you take that bath, you light that candle, and you're really just kind of depressed. And it was making Janey laugh so hard, I just kept going, piling on the self-pity."

Reeves didn't set out to "write a book" with Grant. She was at his house in LA, at a birthday party he was throwing for their mutual friend Janey (Bergam, the book's editor). Bergam passed Reeves's words to Grant without his knowledge. Grant created the images and made them into a book, which she presented to Reeves, hidden inside the pages of a large, green 1970s travel book called The British Scene. "It was a surprise," says Grant, "and a private gift. We didn't make the book to publish it; it was meant to put a big smile on our faces and make everyone laugh. Then someone said, 'I want five copies', and that's when the lightbulb went on."

Reeves, Grant and Bergam contacted the German publisher Gerhard Steidl, and spent four days at his HQ in Göttingen producing the book in-house, as Steidl expects all his clients to do. So what started out as an in-joke is now, well, what? A very expensive piece of fan merchandise? A series of collectible art prints? A parody of a self-help book?

"In your local bookstore," says Reeves, "it could probably go in a number of sections. Self-help? Yeah, absolutely."

"I think of it as a kind of grown-up children's book," Grant adds. "A word that Gerhard kept using was 'haptic'. Why books are so important, especially artists' books, is because they have these haptic qualities: the feel of the paper, the smell of the ink, how it feels to turn the pages. It really is about the artistry."

Ode to Happiness is an undeniably fine object: a stitched brochure, beautifully reproduced on thick paper, in its own clothbound slipcase, and in a limited edition of 4,000 copies, costing £32 each. That's nearly two quid a page. Not exactly value for money, is it?

It depends how you look at it, says Grant. "In terms of drawings, if I did 16 prints that would be pretty expensive."

"And if you think about children's books . . ." adds Reeves. "But I don't even know if this kind of relational, quantity way of talking about it is any good."

"Someone once said it took six hours to write a poem," says Grant. "Five hours 55 minutes on the couch, and five minutes of writing. That's what this project felt like." She turned the words over in her head for a month before putting brush to paper. "I had to figure out how the images could match the text, both in their humour and their darkness."

The illustrations in Ode to Happiness dovetail nicely with Grant's other work: bright, busy, almost synaesthetic arrangements of words penned by collaborating writers, including the poet Michael Joyce. For Reeves, the book is more of a departure. To date, the actor has only strayed out of cinema to work on stage, and to play bass guitar in the bands Dogstar and Becky . "Unless you include being drunk and disorderly," he says. "That's a kind of performance art."

'I'm gonna get deep into haiku'

Will there be more? "I hope we get to do another book," says Reeves. "I'm considering another idea I call Haikus of Hope. Basically like, 'I want to kill myself', and go from there. Going into such a dark place that you can somehow surprisingly find the light at the end of the tunnel – but a nice end of the tunnel. Not the end of the tunnel."

"I have challenges ahead," says Grant. "How am I gonna draw this?"

It seems an appropriate form. Reeves is something of a cryptic haiku himself: an actor who attracts no animosity, despite having had one of the most successful, lucrative and charmed careers in showbusiness. "I hang from a cherry tree . . . I hang," he continues, with mock solemnity. "I'm gonna get deep into haiku, because oftentimes people construe that in English it's five-seven-five syllables, but that doesn't have to hold true, so I want to play with the traditional Basho form. I like that: Haikus of Hope."

"There's a great Japanese tradition called haiga," says Grant, trying to steer things in a serious direction. "Hai as in haiku, and ga meaning painting – painting and text working together. And in this book there's definitely a Japanese sumi-e ink quality to the drawings. So I think we're on to something."

I can't resist asking if Cheer Up Keanu Day was in any way responsible for Reeves's current ebullience. Did he even know about it? "Oh, the internet deal," he says vaguely. "It was brought to my attention. Yeah, it was funny. But no, the book predates that by a long time. We finished it in August 2009. It is hopefully, in a quiet and enjoyable way, transformative. The kind of thing that takes you from this one place to another – to look at yourself and, y'know, it can always be worse. I hate that sentence: of course it can always be worse!"

Reeves hasn't given up his day job just yet. He's currently in London shooting 47 Ronin, a stylised take on a well-known samurai legend. "A story of honour, revenge and love," he calls it. Many have attributed his success to some form of Buddhist detachment, noting his sympathy for the religion, as well as his penchant for zen-like, blank-slate characters: Neo in The Matrix, Ted in Bill and Ted, Bob in A Scanner Darkly, and, er, the Buddha in Bertolucci's Little Buddha. And now we have 47 Ronin and, perhaps, Haikus of Hope. So is there some zen theme guiding his career?

"I guess if you collect some of those strings and hold them in one hand, it can tend to look like a bouquet," he says.

Is that an affirmation or a denial? "You know," he replies, "I think it just is."

• Ode to Happiness is published by Steidl. Reeves and Grant will be signing copies of the book at Waterstone's Piccadilly, London W1, on Saturday at 4pm.