America’s fastest-growing music destination isn’t Nashville or New York, Branson or Austin or New Orleans. It’s Las Vegas.

While Wayne Newton and Celine Dion are still crooning to older crowds in casino showrooms, they’re now joined by a variety of other performers and concerts—major headliners, artist residencies, festivals, dance clubs and rock bars.

“Vegas didn’t have a music scene a decade and a half ago, but that’s rapidly changing,” says Zoltan Bathory, the guitarist for Las Vegas rock group Five Finger Death Punch, which has sold more than three million records. “This city is becoming what it has never been—a cultural center.”

For years, the gambling enclave was a musical backwater, a graveyard for washed-up stars. Music, often, was on the house or deeply discounted. Now the live-music boom is helping the city diversify its economy, reduce its reliance on gambling, and attract younger visitors.

“The days of gambling—of, ‘We’re going to give you free entertainment to get you here to gamble,’ that’s over,” says music-industry veteran Irving Azoff.

Mr. Azoff is spearheading a high-risk plan, announced last month, to build a 17,500-seat arena for music—about the size of a pro hockey or basketball venue. His partners are Madison Square Garden, casino company Las Vegas Sands and Live Nation Entertainment, a concert promoter which owns Ticketmaster. Just weeks before, MGM Resorts International and Live Nation’s rival, Anschutz Entertainment Group, opened the 20,000-capacity, $375 million T-Mobile Arena, the first new arena in two decades.

Soon Las Vegas may boast five arenas, on par with Los Angeles, New York and Chicago. “Vegas used to be another B-city to stop at and play one date,” Mr. Azoff says. “That’s not how people look at it anymore.”

Hip-hop’s biggest star, Drake, will perform at the T-Mobile Arena in September. Grammy-winning alt-R&B act the Weeknd, pop star Bruno Mars and Latin phenom Pitbull have held residencies in Vegas, joining older acts such as Bette Midler and Elton John. When last year’s inaugural Rock in Rio USA festival picked a site, it was Vegas.

On the nightclub scene, celebrity DJs like Calvin Harris play the 4,500-capacity Omnia, which opened last year. Last month, Hakkasan Group, which owns Omnia, opened a 2,000-capacity club, Jewel. One of the nation’s premier dance festivals, the Electric Daisy Carnival Las Vegas, starts later this month in its sixth year.

The growing importance of music in Las Vegas reflects a shift in the economics of gambling. Amid growing competition from casinos around the country and a sluggish economy, gambling revenue on the Las Vegas Strip has fallen for two straight years to $6.3 billion, compared with 2007’s $6.8 billion peak, according to the University of Nevada Las Vegas’ Center for Gaming Research. Twenty years ago, gambling represented 70% of MGM Resorts’ Las Vegas-related revenue; now it’s 30%.

Live music, though, is thriving: 2015 was a record year for the North American concert business, with the top 100 tours grossing $3.1 billion, according to Pollstar. In the age of digital music, fans are paying up to see their favorite acts in the flesh, often buying tickets for big, boozy, multiday events such as music festivals, cruises—and Vegas trips.

“There’s been a recent, greater focus and investment in major headliners at the [Vegas] properties,” says Kevin Bagger, lead researcher with the Las Vegas Convention and Visitors Authority. He says the share of Vegas visitors who went to a show and said they saw a big-name headliner has doubled to 26% in the past two years.

Big names are the draw, but two innovations laid the foundation for Las Vegas becoming a live-music mecca: artist residencies and dance clubs. Residencies, where artists play one venue exclusively instead of touring, have long been perceived as the realm of mature legacy acts and lounge stars, thanks to famous stints by Liberace, Elvis Presley, and Wayne Newton. Before that, Frank Sinatra, Dean Martin, Sammy Davis Jr. and other members of the Rat Pack were always welcome, regardless of how their careers were going at the time.

That perception is outdated. Many of today’s residencies—from Prince’s Vegas stint in 2006 to J.Lo’s “All I Have” shows this year—aren’t “Vegas acts” so much as opportunities to see international stars. Instead of being shunned by artists, Vegas residencies are sought after. Drai’s, a Vegas beach club and nightclub, has a resident-artist roster that includes Future, a rapper whose last two records each topped the overall Billboard charts in the past year.

Residencies used to indicate that a musician’s career was in decline. Now they can take careers to the next level by providing established acts, especially DJs, with an international platform—much like music-festival appearances. Residencies also help artists avoid constant touring, an expensive and grueling pursuit which can lead to overexposure.

“In Las Vegas, the world comes to you,” says Benny Medina, Jennifer Lopez’s manager. J.Lo’s residency at the Axis theater in Planet Hollywood, owned by Caesars Entertainment, has been well-reviewed. During her performances, Ms. Lopez routinely asks fans in the front row where they’re from, and after 20 or so shows, Mr. Medina has heard countless foreign countries.

Older residency acts remain plentiful, but their stints tend to be shorter than a decade ago. Country-music veteran George Strait, who can still fill stadiums, is playing several batches of shows this year and next at T-Mobile Arena, a space larger than is typical for a residency.

Las Vegas always had nightclubs, places where gamblers could have drinks and hear music, but dancing was considered a distraction. That’s changed radically: Vegas’ music scene now owes much to the intense popularity of electronic-dance music, nightclubs and celebrity DJs.

At Jewel, “the programming policy is based on diversity,” says James Algate, vice president of music at Hakkasan Group. If it’s EDM in one room, another might have hip-hop or pop.

Las Vegas’ local scene is also growing. In the past decade Vegas acts the Killers, Panic! At the Disco, Five Finger Death Punch, Imagine Dragons, Jenny Lewis and Shamir have gone national. Five Finger’s latest record hit No. 2 on the Billboard chart in September, riding a current resurgence in the hard-rock genre. In October, they will headline a hometown show at T-Mobile Arena.

Las Vegas has a long history of reinvention, and music isn’t the only way it is diversifying. As recently as the 1980s many dining options in Vegas were little more than $9.99 all-you-can-eat buffets. Now the Strip is loaded with celebrity-chef gourmet spots. Business conventions are still a key driver, and the city is trying to bring in major-league sports franchises. The National Hockey League is expected to announce the addition of a Las Vegas team later this month.

The evolution of this desert city from gambling getaway to music destination dates from casino magnate Steve Wynn’s opening of the Mirage resort in 1989, which placed a greater focus on entertainment, including the huge success of Cirque du Soleil. Then, in 2003, near the height of her fame, singer Celine Dion started the first modern residency at Caesars Palace’s 4,000 capacity Colosseum. She has since done nearly 1,000 shows and grossed more than $550 million in ticket sales, according to Billboard.

After taking a big hit in the recession, the population of Clark County—one of the nation’s fastest-growing before the recession—is expanding again, some 8% between 2010 and 2015, according to demographer Ken Johnson at the University of New Hampshire. That population growth is creating a more supportive environment for local bands and shows. There’s an audience even if tourists aren’t always interested, says Vegas local Mr. Bathory of Five Finger.

Music venues such as Count’s Vamp’d off the Vegas Strip serve a healthy local ’80s rock scene. The Joint in the Hard Rock Hotel and Casino recently hosted residencies by Mötley Crüe, Def Leppard and Guns N’ Roses. Some older rockers from L.A.’s Sunset Strip have actually relocated to Vegas, where homes are more affordable.

“Vegas is becoming the new L.A.,” says Stacey Blades, a guitarist who plays with “Let It Rawk,” an ’80s rock show that has performed at Count’s Vamp’d.

Vegas’ visitors continue pouring in. A record 42.3 million tourists came last year, up more than 1 million from 2014. “You’ve got a different audience every day,” says Bill Hornbuckle, the president of MGM Resorts. Visitors are skewing younger, and with more cash to spend. The average age of a Vegas visitor has been falling—even as America gets older—hitting 47.7 years old last year, from 50 in 2009. Over 25% of visitors reported incomes over $100,000 last year, up from 15% a year before, according to Mr. Bagger of the Las Vegas Convention and Visitors Authority.

If big, expensive music festivals such as the Coachella Valley Music and Arts Festival are becoming more Vegas-like with their resort atmosphere, Las Vegas is becoming, at least for some visitors, a kind of permanent music festival—a pricey music vacation, with good food, and maybe some games of chance thrown in.