In a memo sent Tuesday to Apple employees, Cook said he knew he wanted to hire Ahrendts from the time the two met in January and realized "she shares our values and our focus on innovation."
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.
For instance, in Apple's quarter ending in late June, average revenue per store declined 9 percent from the previous year to $10.1 million. Even more troubling, the retail division's operating profit for the quarter dropped 19 percent from last year to $667 million. Apple ended the period with 408 stores located in 13 countries.
The stores, which are staffed by nearly 42,000 workers, may have been suffering from a management void. Ron Johnson, a former Target Inc. executive credited for turning Apple's stores into a thriving operation, left the company in 2011 to become CEO of J.C. Penney Co. Johnson's successor, John Browett, left Apple in a management shake-up a year ago. Since then, the stores have been under the management of a lower-level executive and the senior vice president job remained vacant.
This will mark the first time that the Apple's senior vice president in charge of its brick-and-mortar stores also will be in charge of the company's online sales.
In his memo to Apple employees, Cook said he never had met an executive capable of doing both jobs until he got to know Ahrendts.
"She believes in enriching the lives of others and she is wicked smart," Cook wrote.
Ahrendts, 53, proved her ability to galvanize a well-established brand during the past seven years working in London as Burberry's CEO.
Burberry, established in 1856, was growing stale until Ahrendts came along to build upon the popularity of its trench coats by adding more flair and panache to the company's fashion line-up.
To help build buzz, the company brought more technology to the catwalk by streaming its fashion shows through online outlets such as Twitter. The strategy boosted Burberry's sales as Web surfers bought the fancy coats, shoes and bags the company previewed.
In the latest measure of Burberry's success under Ahrendts, the company's quarterly results released Tuesday disclosed that sales rose 14 percent to 1 billion pounds ($1.6 billion) in the first half of this year.
Ahrendts worked closely with Burberry's top creative officer, Christopher Bailey, who will become CEO when she leaves.
Although she is now a prominent fashion figure, Ahrendts comes from humble roots. She grew up in New Palestine, Indiana, which was a city with a population of about 2,000 in her youth. She graduated from Ball State University located about 50 miles from her home town.
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Associated Press writer Danica Kirka in London contributed to this story.
