Jenny Erpenbeck and Michael Hofmann have won the 2024 International Booker prize for Erpenbeck’s “personal and political” novel Kairos, translated by Hofmann from German.

Erpenbeck is the first German writer to win, while Hofmann is the first male translator to win. The £50,000 prize money will be split equally between the pair.

Erpenbeck and Hofmann were announced as the winners at a ceremony held at the Tate Modern in London, sponsored by the Italian luxury fashion house Maison Valentino.

Kairos tells the story of a relationship set against the collapse of East Germany. The novel is a “richly textured evocation of a tormented love affair, the entanglement of personal and national transformations”, said judging chair and broadcaster Eleanor Wachtel.

Hofmann’s translation “captures the eloquence and eccentricities of Erpenbeck’s writing, the rhythm of its run-on sentences, the expanse of her emotional vocabulary”, she added.

Erpenbeck said: “Thirty years have passed since the country in which I was born is gone, so I could dare to look back and take my time to carefully research what I lived through without really being aware of it.”

“I got this idea to make a collage of this love story and the historic story”, she added. This gave her the opportunity to examine how things “meant to be true and great” and that had “utopian potential” could turn into “totally failed communication.”

Hofmann said: “I was really lucky to be asked to do this book … And I thank Jenny for trusting me.”

Wachtel said the judging decision was reached with “considerable consensus”, and that the final judging conversation took half an hour. “I was actually surprised at the ultimate unanimity … this was the book that everyone turned to when it came to the crunch.”

Kairos is Erpenbeck’s fourth novel. Her second, The End of Days, won the Independent foreign fiction prize in 2015, which was the precursor to the International Booker prize. Her third, Go, Went, Gone, was longlisted for the International Booker prize in 2018.

Hofmann has also won the Independent foreign fiction prize – in 1995, for his translation of his father Gert Hofmann’s novel, The Film Explainer. He was a judge for the International Booker prize in 2018, the year that Erpenbeck was previously longlisted.

“Kairos is one of the bleakest and most beautiful novels I have ever read,” wrote Natasha Walter in her Guardian review of the novel. “The dark nature of [the] relationship finds expression in Erpenbeck’s characteristically unyielding style. The novel is written in the present tense, a technique that can be flattening when used by lesser writers. In an elegant translation by Michael Hofmann, here it creates a claustrophobic intensity.”

The other books shortlisted for the prize were Not a River by Selva Almada, translated by Annie McDermott; The Details by Ia Genberg, translated by Kira Josefsson; Mater 2-10 by Hwang Sok-yong, translated by Sora Kim-Russell and Youngjae Josephine Bae; What I’d Rather Not Think About by Jente Posthuma, translated by Sarah Timmer Harvey; and Crooked Plow by Itamar Vieira Junior, translated by Johnny Lorenz.

Wachtel was joined on the judging panel by poet Natalie Diaz, novelist Romesh Gunesekera, visual artist William Kentridge, and writer, editor and translator Aaron Robertson.

Previous winners of the prize include Han Kang and translator Deborah Smith, Olga Tokarczuk and translator Jennifer Croft, and Lucas Rijneveld and translator Michele Hutchison. Bulgarian writer Georgi Gospodinov and translator Angela Rodel won the 2023 prize for Time Shelter.

• Kairos by Jenny Erpenbeck is published by Granta (£9.99). To support the Guardian and Observer, order your copy (£8.49) at guardianbookshop.com. Delivery charges may apply.