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Vogue reported on Wednesday morning that Shulman "intends to leave her role this summer."
"Although I have had months to acclimatise to the idea of leaving Vogue, it hasn't made the moment of announcing this any less sad," Shulman said.
"I have been incredibly privileged to have been able to look after such a great magazine for so long and even more to have worked with so many people over those years who have made the experience so interesting and rich."
Vogue said an announcement on her successor is due to follow.
Shulman started at the title as features editor in 1988. After a brief stint as editor of GQ in February 1990, she took the post of editor at Vogue in 1992.
The magazine celebrated its 100th anniversary in 2016. It was marked with a special edition, which featured the Dutchess of Cambridge Kate Middleton on the cover. Shulman was also the focus of BBC documentary "Absolutely Fashion," which provided a unique behind-the-scenes look at the inner workings of the title.
Nicholas Coleridge, managing director of Condé Nast Britain, said:
"Alex has been the longest serving and most successful editor of Vogue in its 100-year history. She has edited the title for a quarter of its existence, through its period of highest ever circulation, and its simultaneous transformation into a global digital brand."
"She has been the towering figure of the British fashion press throughout her tenure: a superb journalist and editor, who understands and exemplifies every quality. Imaginative, hard-working, perceptive and a brilliant leader, Alex is also a valued friend to so many of us. It is impossible to sufficiently express the contribution she has made to Vogue, to Condé Nast and to the British fashion industry."
Shulman added: "It was difficult to decide to leave but 25 years is a very long time and I am tremendously excited that I will now look forward into a different future, but I know that nothing will be quite like the years I have spent at Vogue.