She will join the iPhone and iPad maker as senior vice president for retail and online stores next year, leaving just two female chief executives in the FTSE 100 Index.
Ms Ahrendts spent more than seven years with Burberry, transforming it into a global luxury brand with a growing presence in emerging markets.
The company today revealed 17% growth in underlying retail sales in the six months to the end of September.
Shares in the group fell 6% on the London Stock Exchange today.
Ms Ahrendts, 53, said she is leaving the business, known for its distinctive beige check design, in "brilliant shape". She will be replaced by Yorkshire-born Christopher Bailey, who will also retain his role as chief creative officer.
Ms Ahrendts said she was "profoundly honoured" to be joining Apple, where she will report to chief executive Tim Cook and be responsible for growing the group's retail presence.
She said: "I have always admired the innovation and impact Apple products and services have on people's lives and hope in some small way I can help contribute to the company's continued success and leadership in changing the world."
Her exit in the middle of next year leaves Carolyn McCall and Alison Cooper, the bosses of budget airline easyJet and cigarette firm Imperial Tobacco respectively, as the only remaining female chief executives heading Britain's biggest listed companies.
Ms Ahrendts, who is American, was appointed Burberry chief executive in July 2006 and previously held senior roles at Liz Claiborne and Donna Karan.
She hailed Burberry's management, digital sales, supply chain, technology, brand and creativity. "Burberry is not only a great brand, but a truly great company," she said.
Mr Bailey, who joined Burberry in 2001, has been chief creative officer for six years. He has overseen all customer-facing activity at the group, including product design and marketing.
"I am profoundly moved and humbled to be asked to take on the chief executive role at this company that means so much to me," he said.
"Together, we will continue to push the boundaries of design, technology and communication while never forgetting our heritage, our Britishness and our values."
Burberry said it was pleased with trading during the six months, as total sales climbed 14% to £1.03 billion.
The 17% growth in its retail business comprised 13% like-for-like growth from stores, with new openings making up the balance.
It saw double-digit retail growth across Asia Pacific and its Europe, Middle East, India and Africa regions, while sales in the Americas grew in high single digits.
Sales of outerwear, such as its famous trench coat, and large leather goods drove half of its growth.
With China's economy slowing, Ms Ahrendts said the group remains wary about the global economy.
"We expect the external environment will remain uncertain and currencies volatile," she said.
Wholesale revenues, excluding beauty sales, fell 7% to £244 million.