Burton joined the label in 1996, just four years after it was founded, and became head of women's collections in 2000.
She "kept and continued Lee's heritage, attention to detail and unique vision, while adding her own personal, highly creative touch," said Francois-Henri Pinault, CEO of Kering, which also includes flagship labels Gucci and Saint Laurent.
Her last show will be the Spring-Summer collection at Paris Fashion Week later this month, Kering said, adding that "a new creative organisation" will be announced "in due course".
The change comes amid a downturn for the luxury giant.
It saw a 10 percent drop in net profits in the first half of the year, driven largely by a decline in Gucci sales.