A seller of high-priced raincoats selling tablets and smartphones?
But when looked at through the prism of the fast-changing luxury industry, Ahrendts is the perfect hire. That's because Apple has become a luxury brand first and a technology company second.
The latest CoolBrands survey in Britain—compiled by a panel of 27 experts and 2,000 consumers—ranks Apple as the No. 1 brand. It's followed by more traditional luxury brands, with Aston Martin ranking second and Rolex ranking third. (Burberry doesn't make the top 20).
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Luxury experts say that today, luxury is defined more by performance and design than by status badges, logos and history.
"I have always thought of Apple as a luxury brand," said Greg Furman, founder and chairman of The Luxury Marketing Council. "They have the hearts and minds of today's most affluent consumers."
He added, like luxury companies, Apple's marketing is "image driven and highly creative." The company also has "impeccable products, service and merchandising," like the best luxe brands, Furman said.
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Apple's luxury aura is especially strong among the newer wealthy. A study of 1,000 consumers with a median income of $200,000 by Dwell Strategy & Research found that Apple ranked first among the favorite brands. More traditional luxury brands followed further down the list: BMW, Porsche, Chanel and Ralph Lauren.
"This generation of nouveau riche is shunning 'conspicuous consumption' in favor of brands that represent quality, aesthetics and authenticity," advertising industry veteran Tim Arnold wrote in Advertising Age. "These attributes, along with uniqueness, integrity, design and performance, represent today's 'prestige' for these high-end consumers."
If Apple has already mastered the luxury game, why does it need Ahrendts?
One reason may be the company's entry into the "wearables" market, with watches and other devices. Having an executive who has reinvented a storied luxury brand through better design, quality and digital and social media can only help—especially on the retailing side.
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But Furman and others say the company may be looking for Ahrendts to bring fresh ideas to a company that's always looking for an edge.
"Apple is always looking to up their game and [give] that extra oomph," Furman said. "I think she can bring that."
—By CNBC's Robert Frank. Follow him on Twitter: @robtfrank.