SAN FRANCISCO — Apple is entrusting the elegant stores that help define its brand to Angela Ahrendts, a respected executive who blended fashion sense with technological savvy to establish Burberry as a mark of luxury and success.

The hiring announced Tuesday is a coup for Apple Inc. Besides providing the Cupertino, Calif., company with another sharp mind, Ahrendts should help Apple deflect potential criticism about the lack of women in the upper ranks of its management.

Silicon Valley’s long-running reliance on men to make key decisions has come into sharper focus as online messaging service Twitter Inc. prepares to go public.

Twitter’s closely scrutinized IPO documents called attention to the San Francisco company’s all-male board of directors and the presence of just one woman in its executive inner circle.

Apple has one woman, former Avon Products Inc. CEO Andrea Jung, among the eight directors on its board.

Ahrendts will report directly to Apple CEO Tim Cook when she leaves Burberry to join Apple next spring in a newly created position of senior vice president in charge of retail and online stores.

Ahrendts telegraphed her admiration of Apple in 2010 when The Wall Street Journal asked her if she was trying to mold Burberry into something similar to other luxury brands in the fashion industry.

“I don’t look at Gucci or Chanel or anyone,” Ahrendts told the Journal. “If I look to any company as a model, it’s Apple. They’re a brilliant design company working to create a lifestyle, and that’s the way I see us.”

Ahrendts’ arrival comes at a crucial time for Apple and the stores that serve as the main showcase for its iPhones, iPads, iPods and Mac computers.

Like the rest of the company, Apple’s stores aren’t doing quite as well as they once were, primarily because tougher competition has forced the company to trim its prices.