It’s the era of the million-dollar hip-hop deal.

Over the past 12 to 18 months, competitive pressure has pushed the cost of signing a new rapper up threefold, music-industry insiders say. The biggest contracts for debut artists, once capped at $1 million, can hit the double-digit millions.

“In 2017, some of the first guys getting signed were [receiving] less than a $200,000 advance” for their first album, says Tariq Cherif, co-founder of Rolling Loud, one of hip-hop’s biggest festivals. “Now you’ve got guys that nobody’s ever heard of—they’ve got one music video that goes viral—and they’re getting deals for multiple millions of dollars.”

Hip-hop dethroned rock as America’s most popular genre last year, putting pressure on labels to expand their rap rosters to build market share. Feeling flush from an industry rebound fueled by music-streaming, executives are scrambling to sign buzzy rappers before competitors do.

Artists increasingly have leverage in deal negotiations, music-industry insiders say, thanks to streaming successes and powerful attorneys and managers. They’re demanding heftier advances, shorter contracts and lucrative profit splits. Often, they’re rejecting traditional deals where labels own the recordings and receive the lion’s share of royalties and instead seeking temporary licensing agreements where they retain ownership.

The hip-hop bidding wars are a new chapter in the until-recently moribund U.S. record industry, even if overall revenues remain 40% lower than their 1999 peak.

Just as music executives once chased “hair-metal” bands (1980s), grunge groups (1990s) and anything resembling the Strokes (early 2000s), they’re now grabbing rappers with face tattoos, social-media fame and a lo-fi, melodic sound associated with the streaming service SoundCloud. If you’re in a music video with a famously morose rapper, it could land you a deal.

Acts like rap collective Brockhampton and the recently murdered Florida rapper XXXTentacion with a reverent fan base or massive streaming numbers command huge money because they’re seen as safe bets.

But there’s also “a lot of froth,” says Peter Edge, chief executive of RCA Records, which signed Brockhampton and Childish Gambino. “The music business has always been known to get a little overexcited.”

The swiftness of star-making in the social-media age and widespread reliance among labels on data from YouTube, SoundCloud and Spotify mean executives quickly swarm over the same acts and overpay to win bidding wars, insiders say.

In March, Young Nudy, a 25-year-old cousin of Atlanta rap star 21 Savage, signed with labels RCA Records and SamePlate for a four-album, multimillion-dollar deal, according to his manager, Trevor Patterson.

The same month, in one of the industry’s most touted deals, 19-year-old Chicago rapper Juice WRLD signed a multimillion-dollar partnership with labels Interscope Records and Grade A Productions, according to a person familiar with the situation. “Lucid Dreams,” Juice WRLD’s biggest single, has been a smash hit, reaching No. 3 on the Billboard singles chart.

Other rappers that have fueled bidding wars include California’s Yung Pinch and Florida’s Dominic Fike, music-industry executives say.

One of the most aggressive labels to sign new acts has been Atlantic Records, part of Warner Music Group, the record industry’s third-biggest company. Atlantic has signed hitmakers Cardi B and Lil Uzi Vert and emerging acts Lil Skies, Shoreline Mafia and Rico Nasty, according to people familiar with the matter. Independent distributor and label Empire has made waves by offering acts artist-friendly deals.

Some labels are proceeding cautiously. Executives at Mass Appeal Records, an independent label co-founded by veteran rapper Nas whose roster includes more lyrically-minded acts like Run the Jewels and Dave East, are launching a new imprint, Street Dreams, in partnership with Nas’s younger brother, Jabari “Jungle” Jones, to sign a broader array of new acts. “We’re not going to put out a bunch of guys that look the same,” Jungle says.

For many acts, it’s still tough to get a record deal. Contracts vary depending on details like the number of albums, front-end advances and recording budgets. Rappers may exaggerate deal sizes publicly for marketing purposes. And some artists, like 21 Savage, who has a joint venture with Epic Records, have rejected big-money offers in favor of partnerships, says his manager, Kei Henderson.

Industry executives are already speculating about how long the bidding frenzy can last. “At some point, is this a bubble?” says John Ingram, a music-industry lawyer. “And if so, when will it burst?”

As labels enlarge their rosters, executives may lose the bandwidth to develop individual artists, especially those who aren’t immediately hitmakers, says Ibrahim Hamad, who manages rap star J. Cole.

The music industry has changed considerably over the past decade and record labels may be justified in ramping up their investments, some executives say. Global distribution of music today is cheap compared with the days of physical CDs and records, making profit margins better. Rap doesn’t require large studio budgets, and radio promotion—a significant label expense—is no longer essential. In some cases, deals can pay off quickly.

With the record industry’s rebound driven almost entirely by the rise of streaming services, labels need to invest in the relatively new music popular on Spotify and other platforms, some executives say. Hip-hop represents 38% of U.S. on-demand audio streams, Nielsen Music says, more than rock (20%) or pop (16%).

“All those great catalogs we have from the ‘60s, ‘70s and ‘80s—it’s not translating over to streaming numbers,” Mr. Ingram says.

But critics have begun complaining that the rap frenzy is creating a glut of gimmicky, relatively interchangeable artists. “A lot of it sounds the same,” says Empire A&R executive Tina Davis. Labels “sign five of the same thing, to see which of them will work,” she says. “They’re grabbing them and throwing them at the wall like spaghetti.”