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 also revealed 17% growth in underlying retail sales in the six months to the end of September with sales of outerwear, such as its famous trench coat, and large leather goods driving half its growth. Total sales climbed 14% to £1.03 billion.
Fifty-three-year-old Ms Ahrendts said she was leaving the business 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 female chief executives in the FTSE 100.