Born in Rome, after Albinati started his career as a translator, a script adaptor and editor of the magazine Nuovi Argomenti.

He made his debut as a writer in 1988, with a collection of short stories titled Arabeschi della vita morale.

His 1989 novel Il polacco lavatore di vetri was adapted into a film, The Ballad of the Windshield Washers by Peter Del Monte.

[2] In 2002 and in 2004 he took part to two UN High Commission for Refugees missions in Afghanistan and Chad, also writing several reports published by the newspapers Corriere della Sera and La Repubblica.

In 2016 he won the Strega Prize with the semi-autobiographical novel La scuola cattolica.