Szalay, who was previously shortlisted in 2016 for All That Man Is, received STG50,000 ($A100,822) and a trophy, presented to him by last year's winner Samantha Harvey.
Written in spare prose, Flesh follows a man caught in a series of events beyond his control as it charts his rise from a housing estate in Hungary to the mansions of London's super-rich.
"A meditation on class, power, intimacy, migration and masculinity, Flesh is a compelling portrait of one man, and the formative experiences that can reverberate across a lifetime," organisers of the award ceremony in London said in a statement.
Flesh is Szalay's sixth work of fiction and he says the novel's central character is written from the perspective of an outsider.
"Even though my father is Hungarian, I never felt entirely at home in Hungary. I suppose, I'm always a bit of an outsider there and living away from the UK and London for so many years I also had a similar feeling about London," Szalay told BBC Radio.
"I really wanted to write a book that stretched between Hungary and London and involved a character who was not quite at home in either place."
Former Booker Prize winner and chairman of the judges, Roddy Doyle said: "The judges discussed the six books on the shortlist for more than five hours.
"The book we kept coming back to, the one that stood out from the other great novels, was Flesh - because of its singularity. We had never read anything quite like it. It is, in many ways, a dark book but it is a joy to read.
"I don't think I've read a novel that uses the white space on the page so well. It's as if the author, David Szalay, is inviting the reader to fill the space, to observe - almost to create - the character with him.
"The book is about living and the strangeness of living, and, as we read, as we turn the pages, we're glad we're alive and reading - experiencing - this extraordinary, singular novel."
The Book Prize panel considered 153 books and was looking for the best work of long-form fiction by writers of any nationality, written in English and published in the UK and/or Ireland between October 1, 2024 and September 30, 2025.
Previous winners of the Booker Prize include Salman Rushdie, Kazuo Ishiguro, Margaret Atwood and Dame Hilary Mantel.
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