He will hold the role of general manager and chief executive at the Milan-listed luxury group.
Burberry said Gobbetti is stepping down after nearly five years in the FTSE 100 group to take up another opportunity so he can return to Italy and be closer to his family.
It will now begin the search for a successor, while Gobbetti will work with chairman Gerry Murphy to ensure an orderly transition.
The 62-year-old has been in the fashion industry for decades, as he became chief executive of Burberry after holding the same role at Moschino, Givenchy and Celine.
“The board and I are naturally disappointed by Marco's decision but we understand and fully respect his desire to return to Italy after nearly 20 years abroad,” said Murphy.
“With the execution of our strategy on track and our outlook unchanged, we are determined to build on Burberry's strong foundations to accelerate growth and deliver further value for our shareholders."
Shares plunged 9% to 2,040p on Monday morning.
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