FRANKFURT—Germany's Adidas AG is placing a costly bet on catching up with its rivals in the digital fitness world, agreeing to pay €220 million ($239 million) for Runtastic GmbH, an Austrian fitness app maker.

The world's second-largest sporting goods company, which claims it was the "first in the industry to comprehensively bring data analytics to the athlete," hopes the acquisition will pump up interest in its brands and turn some of Runtastic's 70 million users into Adidas footwear and apparel shoppers.

"There is no doubt that the digital world is conquering our industry," Chief Executive Herbert Hainer said Thursday. "Just looking at Runtastic numbers gives a decent impression of how many consumers one can attract."

Adidas doesn't want to be outrun in digital growth, judging from the price tag. Among the sellers is publisher Axel Springer, which bought a 50.1% stake in Runtastic in 2013, when its enterprise value was just €22 million.

Runtastic was founded in 2009 in Pasching, Austria, and entered the fitness app movement early. It now offers more than 20 fitness, health and endurance apps, including Leg Trainer, Six Pack, and Sleep Better, which tracks sleeping patterns. It also recently branched into hardware.

Adidas isn't the only sportswear maker betting apps will inspire enthusiasm for its products. The purchase comes only a few months after its U.S. rival Under Armour Inc. invested $710 million in its Connected Fitness platform. The platform consists of health and fitness app companies MapMyFitness, which Under Armour acquired in 2013, and Endomondo, and MyFitnessPal, which it bought in early 2015. MyFitnessPal cost $475 million and was Under Armour's biggest acquisition.

Nike Inc., Adidas's most formidable competitor, has been a pioneer in fitness tracking, and teamed up with Apple Inc. early on. People who use the Nike+ Fuel app can track their fitness on the most recent iPhone.

Adidas launched its own fitness device mi Coach last year, but has been losing market share, particularly in North America. Last fall, it fell behind Nike and Under Armour to the third spot in U.S. apparel and footwear sales, according to figures collected by SportScanInfo and Sterne Agee.

"There has been a move toward more consolidation in connected fitness for some quarters now," said Cé dric Rossi, an analyst at Bryan Garnier in Paris. Increasingly, active people want to track their performance and data, he added. "Adidas obviously doesn't want to lose out in that market."

More often than not apps are free, like Adidas's mi Coach Train and Run app, but they can pay off by letting manufacturers cash in on sales of matching hardware. The mi Coach Fit Smart armband, for example, costs about $150.

Runtastic will continue to operate as it successfully has to this point in time, Adidas said, adding "we will determine the best path to ensure Runtastic users and Adidas mi Coach users continue to enjoy great experience, services and products."

Matt Powell, a sports-industry analyst for NPD Group, believes the play for sports brands is more software than hardware. "The key to leverage will be how well they brand Runtastic with Adidas," he said.

Both Mr. Powell and Mr. Rossi said buying Runtastic is a good move for the German company, if an expensive one.

"There has been a huge inflation in the category," Mr. Rossi said.

Unlike other free fitness app companies, Runtastic has been profitable from the starting gate, Adidas said, which helps explain the price tag.

Adidas said Runtastic will continue to operate as an independent business unit, and all its four co-founders will stay on board for at least three years.

The German sportswear maker reported second-quarter earnings on Thursday. It said profit rose slightly, while sales grew 5% compared with the year before.

Write to Ellen Emmerentze Jervell at ellen.jervell@wsj.com

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