As Harry Potter, actor Daniel Radcliffe was the boy wizard who lived in the cupboard under the stairs. Now, he’s an angel working in the basement of heaven.

In his new show, the TBS comedy “Miracle Workers,” Mr. Radcliffe plays Craig, a low-ranking angel at Heaven Inc., who diligently answers humanity’s prayers. He and other angels must try to save Earth after their capricious boss, God (Steve Buscemi), decides he wants to blow it all up and start a new venture.

There’s a lot of collateral damage as their mission unfolds—a single action in heaven can trigger a natural disaster or wave of accidental deaths on Earth. The show pokes fun at the randomness of earthly encounters and human culture. “It manages to be both nihilistic and very positive at the same time,” Mr. Radcliffe says. “That’s something akin to my outlook, which is that yes, the world is crazy but we’re so lucky to be alive.”

“Miracle Workers” is his first major comedy on screen; he’s also an executive producer of the series, which debuts Feb. 12. It’s intended to be an anthology, like the dramas “True Detective” or “American Horror Story,” with each season (if the show succeeds) taking on new story lines, settings and characters, while keeping many of the same actors.

The prospect of changing characters is a big part of the appeal for Mr. Radcliffe, who had long wanted to do an American television series but was reluctant to play the same part over and over again. “Having played one character for a long time when I played Harry, this felt like an amazing opportunity to get into TV, but also get to do something new every year,” he says.

As Harry Potter, he played in eight films for a decade, from the age of 11 to 21. Getting cast as the orphan wizard brought Mr. Radcliffe, now 29, instant, international fame. Yet being on the set for 11 months of the year “isolated me from the outer effects of what fame is,” he says. “I also think that if you can become famous when you’re young, and do it with good people around you, you know, you can throw a kid into anything and they’re very adaptable.” He thinks a film set is the place where actors get treated normally, since everyone else working on the set is used to being around actors: “There’s nothing special about it.”

He also worked out, early on, what success means to him. “I’ve always been very lucky, very young, to be financially secure and to work on really big movies,” he says. “I know that is amazing, but it’s not the be all, end all of what a successful life as an actor looks like to me. It’s about longevity and versatility and having fun.”

Since the “Harry Potter” franchise concluded in 2011, he has worked in a range of films and starred in theater in New York and London, including Broadway’s “How to Succeed in Business Without Really Trying” and “The Lifespan of a Fact,” where he tried to hone his comedic delivery every night. In “Lifespan,” which closed Jan. 13, he played an obsessive fact checker at a magazine, opposite Cherry Jones and Bobby Cannavale.

“There were some nights when it felt like we were doing a sitcom with a live audience,” he says. “I love doing theater in London, but New York audiences are so vocal, man!”

With theater, the jokes don’t always land with live audiences, and in a play full of them, the risk is high. “When you lay yourself out for a joke and you get nothing, you feel very cheap,” he says, grimacing at the thought of it. “I have a very jarring response whenever that happens,” he says as he throws his arms up in the air and shields himself. “It’s a thing you learn early on, not to chase jokes. That’s part of the ebb and flow of doing a show every night. But as an actor, you get attached to certain laughs,” he says.

Although “Miracle Workers” is his biggest foray into on-screen comedy, he has made guest appearances on “The Simpsons,” hosted “Saturday Night Live” and had a dog-walking cameo in “Trainwreck.” (“The amount of people that mention that to me is amazing still,” he says of the cameo, marveling at the half-life of a half-day’s work.)

As a viewer, he has long devoured sitcoms, he says. He grew up on Alan Partridge and “The Day Today,” “The Office” (the British one), and “Fawlty Towers.” As a teenager, he’d rush home every day to catch “The Simpsons” on BBC Two. “‘The Simpsons’ is my baseline for comedy. Me getting to do a voice was a real ‘I made it’ moment,” he says.

“Miracle Workers” mines dark territory, with both the angels and humans dealing with their own demons. Mr. Radcliffe sees comedy as a coping mechanism for sadness and thinks that characters like David Brent in the British “Office” (played by Ricky Gervais) and Alan Partridge (Steve Coogan) are “brilliantly tragic creations” and “all about desperation to be liked.”

In his spare time, Mr. Radcliffe doesn’t find it relaxing to watch movies; it’s stressful to see Oscar-nominated pictures or performances, he says, though he did see “Vice” and loved it. “I get a bit, ‘I wish I were in that,’ or ‘I’m not working hard.’ It’s a funny feeling,” he says.

His eyes light up, though, when discussing favorite documentaries, and he confesses to consuming a lot of “semi-trashy TV.” “I’m unashamedly into ‘The Bachelor.’ ‘Top Chef,’ I’m obsessed with,” he says.

He’s also a big sports fan. On Super Bowl Sunday, he’ll be supporting the Rams. “The Patriots now are like Manchester United in the ’90s in England, where they’ve just been too good for too long, and we all have to start rooting for their demise,” he says.

As for his own faith, Mr. Radcliffe says that he doesn’t expect there to be an afterlife, or a God. “I feel like people think that being agnostic is depressing and bleak, and I’ve never found it to be that way,” he says. “It always seems to me that there being nothing after just makes this incredibly special…It does seem miraculous.”