The British-Hungarian author's sixth novel, which follows the life of an inscrutable Hungarian man, was unanimously chosen by the judging panel for its unique style and exploration of modern masculinity.
Roddy Doyle, chairman of the Booker judging panel, lauded Flesh for its "singularity", with Gabby Wood, chief executive of the Booker Prize Foundation, describing it as "spare, disciplined, urgent, honest and heartbreaking".
Szalay will receive £50,000 in prize money, despite Andrew Miller's The Land in Winter having been the bookmakers' favourite to win.
The 2025 shortlist notably featured only established authors, with no debut novels, and included works by Kiran Desai, Ben Markovits, and Katie Kitamura.