It’s the latest “old timey” hobby to gain a dedicated new following.

Step aside, goat yoga. The chic way to unwind now is fly fishing.

That’s right. For some of the same reasons millennials recently flocked to bird-watching, this sport — long dominated by old white men — is gaining popularity with a younger set.

For those who can afford the leisure time and some rudimentary equipment, it offers a reason to be outdoors, a closer connection to nature, an avenue for environmentalism, built-in community, opportunity for creative expression, and a lifetime’s worth of niche expertise. Fly anglers who are not vegetarian nor vegan, nor otherwise bound by the code of “catch and release,” see it as an extension of the farm-to-table movement. Plus, it’s very Instagrammable, even as it encourages people to put down their phones.

And where millennials go, hospitality brands follow. Guided fly-fishing excursions are now offered at many trendy boutique hotels, including The Little Nell in Aspen, Colo.; Tourists, the eco-friendly lodge opened by indie influencers including the bassist of Wilco, in North Adams, Mass.; and Sage Lodge, a new nature resort just north of Yellowstone National Park in Pray, Mont., which has a stand of fly tackles and nets in its lobby, and daily “Fly Fishing 101” courses at its backyard casting pond overlooking the Absakora Mountains.

At the DeBruce, a boutique hotel and culinary destination in Livingston Manor, N.Y., the wall art, bookshelves and nine-course tasting menu are fly fishing-themed. The banner amenity of the hotel, where rooms start at $449 a night (including breakfast and the tasting menu), is half a mile of private river; waders, rods and reels are all available for rental for $75 per day in the Tackle Room near the pool. And in the Great Room, where elegant young couples on honeymoons, babymoons and minimoons pass their happy hours, a full fly-tying station is set up in the corner.

Todd Spire, 45, a digital marketer turned full-time fly guide, has built his Catskills business on this new wave of interest. Over the past 4 years, his guiding outfit, Esopus Creel, grew steadily by word-of-mouth and Instagram, and this spring, he opened a brick-and-mortar fly shop in Phoenicia, N.Y.

“You have millennials who are drawn to experiences, looking for authentic ways to experience this place, and you have this activity which is such a big part of both this area’s history and its conservation,” Mr. Spire said. And, he noted, the area is of historic importance to the sport. “Almost every aspect of fly fishing was refined, changed, evolved in the Catskills.”

And indeed, when clients fish in the Esopus Creek with Mr. Spire, they’re waist-deep in the same waters where Babe Ruth fished during the late 1930s. Decades before that, pioneering sportsmen like Theodore Gordon and Edward Ringwood Hewitt fished on the Neversink River. Nearby, on the Beaverkill River, the inventor of the fishing vest, Lee Wulff, perfected the use of his namesake flies, while his wife at the time, Joan Wulff, a competitive angler, brought novel poise and femininity to the craft of casting them. (She once cast a cigarette out of Johnny Carson’s mouth on the daytime game show “Who Do You Trust?”) Ms. Wulff, now in her 90s, still teaches at the 40-year-old school they founded, run out of a cabin near Livingston Manor.

“I’ve become completely addicted to fly fishing,” said Mike Kauffman, 31, a tech entrepreneur and Manhattan resident who recently bought a home in the Catskills with his girlfriend, Annah Lansdown. “I find it totally meditative — the thing I never knew I needed.”

When he started out this spring, Mr. Kauffman knew virtually nothing about the sport: “I was at Phoenicia Diner and I saw ‘Esopus Creel’ on their menu,” he said, referring to an ad. “I thought, ‘Oh man, they spelled creek wrong.’”

But from his first guided outing with Mr. Spire, Mr. Kauffman and his girlfriend were hooked. “We’re scrolling all day thinking we’re connecting with the world, but our minds aren’t satisfied,” he said. “Being out in that river is a deeper connection to nature I never really had — and I think a lot of people don’t have. It’s something our monkey brain needs.”

Ms. Lansdown, 41, a creative director at a digital agency, added, “The water’s rushing around you, and you can’t hear anything. You can’t even hear people yelling at you. You don’t think about work, or emails, or the city.”

Now, the couple owns all the gear.

And there’s plenty of gear and apparel to own. Newcomers may require waders, vests, tackle boxes, rods, reels, creels, flies and perhaps even fly-tying equipment. Graphite rods can cost as little as $30 but classic bamboo rods — preferred by Brad Pitt in the 1992 movie “A River Runs Through It” — can cost thousands. (For those seeking the highest-end option, Hermés recently debuted a wooden fly rod, priced at $13,790, and a wicker and calfskin creel for $17,420.)

“I can’t put my finger on what it was, but about five years back, something changed,” said Joe Fox, 33, a manager at Dette Flies fly shop in Livingston Manor. “Especially in the past three years, we started seeing more new faces.”

According to the 2019 Outdoor Industry Association’s “Special Report on Fishing,” fly fishing is the fastest-growing category of the sport. Gender and racial diversity continues to tick upward. Age diversity encompasses both categories. Last year, one in four anglers surveyed were in the 18 to 34 age range.

Mr. Fox recently took over the family fishing supply business from his grandmother, who’d herself taken over from his great-grandparents, Winnie and Walt Dette. He launched a web store, and this past year, he and his partner, Kelly Buchta, also a fly angler, moved the business, which had been in the Dette family home in Roscoe, N.Y. since 1928, to a spacious new store on Livingston Manor’s main street. Longtime customers have stayed loyal. New customers continue to arrive.

In 2011, the store experienced a surge of attention shortly after celebrities like Selena Gomez and Steven Tyler, for inexplicable reasons, got into weaving grizzly saddle hackles — long, thin, speckled rooster feathers — through their hair. In short time, the style went viral. Shops like Dette began to sell out of their fly-tying supplies, and in the lead-up to Bonnaroo that spring, virtually nobody could keep feathers in stock. Prices spiked. Some anglers were furious; others took to eBay with their spare hackles, selling them for ten times the buying price.

This time, the newcomers are buying Dette’s wares for their intended purpose.