It is understood that Ahrendts will report directly to Tim Cook, Apple's chief executive, when she leaves her position at Burberry in mid-2014.
Christopher Bailey, who has been chief creative officer at the British fashion house for six years, will take over from Ahrendts when she departs. He will retain his responsibilities and become chief creative and chief executive officer.
Burberry said Ahrendt’s departure follows nearly a decade during which she, Bailey and the senior executive team have "transformed Burberry into a world leading digital luxury brand".
Bailey, who has been with the company since 2001, has overseen all consumer-facing activities, including project design and development, creative marketing, store design, consumer technology and digital innovation.
He will continue to create and drive the company’s vision and will work closely with Ahrendts over the coming months to ensure a seamless transition, and will join the board in due course.
Today Burberry announced a 17% growth in underlying retail sales in the six months to the end of September, while total revenue grew 14% to £1.03bn.
This year Ahrendts topped the chief executives’ earning list within the FTSE 100, becoming the first woman to top the City pay league with £16.9m earnings, though this was reportedly due to her selling nearly £12m worth of Burberry shares.
Ahrendts said: "Burberry is in brilliant shape, having built the industry's most powerful management team, converted the business to a dynamic digital global retailer, created a world class supply chain, state of the art technology infrastructure, sensational brand momentum and one of the most closely connected creative cultures in the world today.
"It has been an honour to have partnered with [chairman] Sir John Peace and Christopher for the past eight years.
"I am confident that, with Sir John's continued guidance and the executive team's support, Christopher, as one of this generation's greatest visionaries, will continue to lead Burberry to new heights.
"Today, Burberry is not only a great brand, but a truly great company."
Watch Burberry chairman Sir John Peace discussing the changes with Angela Ahrendts and Christopher Bailey in the video below.