Justin Theroux is the main course in ‘The Leftovers’

Reporting from NEW YORK —  For most of the last two decades, Justin Theroux has dwelled happily in the Hollywood sweet spot between obscurity and mainstream celebrity. The multi-hyphenate stayed busy with roles in projects as varied as the frothy action flick “Charlie’s Angels: Full Throttle” and the lofty miniseries “John Adams” while forging a second career as one of the industry’s most in-demand screenwriters.

Then — and don’t pretend you don’t know this already — Theroux suddenly became a paparazzi magnet when he got engaged to a little-known actress by the name of Jennifer Aniston.

But the new series “The Leftovers,” premiering June 29 on HBO, finds Theroux in uncharted territory as a leading man. The drama from “Lost” creator Damon Lindelof and based on Tom Perrotta’s novel of the same name takes place three years after 2% of the world’s population spontaneously vanished in an unexplained cataclysm. The event, with strong 9/11 overtones, seems too random to qualify as the Rapture yet is devastating enough to have left survivors reeling.

Theroux plays Kevin Garvey, the chief of police in a fictional New York suburb where a mysterious cult-like group has taken hold and a family man struggling to rein in his angsty teenage daughter.

“I’m more of a character actor in a way,” says Theroux, 42, over a late lunch not far from the downtown apartment he keeps in the city. (These days he’s bicoastal.) An unusually eclectic resume supports that claim. In his early years in New York, the Washington, D.C., native primarily made his living as a painter but switched to acting full time after starring in a well-received off-Broadway show about Beatles manager Brian Epstein.

After small roles in “I Shot Andy Warhol,” “American Psycho” and “Sex and the City,” a breakthrough arrived when Theroux played a cuckolded filmmaker in David Lynch’s surrealistic riddle “Mullholland Drive.” He later starred in the director’s even more impenetrable “Inland Empire” and calls working with Lynch “the closest thing you can get to a sense of true discovery on a set.”

Though “Mulholland Drive” played on his noirish, menacingly handsome looks — the widow’s peak, the dramatically arched eyebrows — and cued him up to be Hollywood’s next Serious Leading Man, Theroux has continued to carve an unpredictable career path, alternating between quirky comedy and highbrow drama and even directing a feature film, the indie romance “Dedication,” in 2007.

He says he’s avoided being pigeonholed only because he’s “terrible about making calculated choices” about his career. “It’s served me well to be more fluid in my approach — just to do the next thing that makes you happy and is satisfying.”

The actor, bearded and draped in beads, last starred as a charismatic but clueless commune leader in David Wain’s 2012 farce “Wanderlust,” where he mused philosophically about the corrupting influence of modern technology — things like Nintendo power gloves, answering machines and laser discs. According to Wain, Theroux was an expert at improvising in front of the camera — particularly the “really weird creepy monologues” delivered to Aniston’s character — and also provided invaluable input on the script. “Justin has a great instinct just for finding a spine for a scene, and he definitely has an ear for dialogue.”

“I love to play people who are way more confident than they are intelligent,” says Theroux, who played similarly hirsute buffoons in the stoner comedy “Your Highness” and the biblical spoof “The Ten.”

Since “Wanderlust,” he has focused primarily on screenwriting, a vocation he came to through his long friendship with Ben Stiller. The pair spent years developing the idea that would become “Tropic Thunder,” the hit 2008 action-comedy. Theroux has since racked up numerous writing credits, including “Iron Man 2” and “Rock of Ages,” and he and Stiller are working on a long-gestating sequel to “Zoolander.”

Writing seems to be in the blood: His mother is essayist Phyllis Theroux (she once wrote a piece for the New York Times about how her son, looking “a little like Nathan Detroit,” took two dates to the eighth grade formal), and his uncle is the bestselling travel writer and novelist Paul Theroux. But Theroux sees little in common between their “really smart” work and his own. “I don’t do what they do at all, nor could I.”

Despite his growing reputation as one of the industry’s brightest comedic talents, in person there are few flashes of the caustic wit that brought us “Tropic Thunder’s” infamous “Never go full retard” speech. Likewise, despite his rebellious affectations — preternaturally black hair, a Dead Kennedys T-shirt, Doc Martens with red laces — Theroux comes across as highly disciplined. He shows up early to our meeting, has a tendency to break his sentences down into lettered bullet points and his major vice appears to be a compulsive Nicorette habit.

In this sense, playing a stoic Everyman type in “The Leftovers” — a character whose emotional journey Theroux likens to a “washing machine on spin cycle that just starts to become unbalanced” — may not be as much of a stretch as it seems.

“It’s a very hard part because he’s not a character who talks in these grandiose terms about his interior emotional life,” says show runner Lindelof, “he’s not diagnosed with lung cancer and dealing meth, or some kind of corrupt cop who goes around beating people up.”

Co-star Amy Brenneman, who plays a woman in the grip of the town cult, praises Theroux’s “vulnerable masculine presence” on camera. “A lot of men either they don’t have the natural charisma and strength, or more often, to be honest, if they have the charisma they cannot access the vulnerability.”

“The Leftovers” will be Theroux’s first regular series role since spending an unsatisfying year and a half on the “very down the middle” CBS drama “The District” in the early aughts. Between the intriguing material, a chance to return to HBO, where he has become something of a repertory player, and a 10-episode season that will allow him plenty of time to write, the project is a “perfect storm,” he says.

“The Leftovers” will also provide the opportunity to step out of his supermarket tabloid role as Jennifer Aniston’s fiance — though truthfully he doesn’t seem too concerned about that.

“I acknowledge exactly what it is: bread and circus for a certain segment of the population,” he says of the focus on his personal life. “There are many, many worse things.”

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