Saverio Costanzo was born in Rome on 28 September 1975 and graduated in Sociology of Communications from La Sapienza University of Rome. After various experiences as a radio host, television scriptwriter for RAI series, and director of several commercials, he moved to New York at the end of the 1990s. There, he produced a documentary series, recreating the daily life of Italian-Americans at Caffè Milleluci in Bensonhurst, Brooklyn. Caffè Milleluci was the first Italian example of a docu-soap created for the internet. In 2000, Costanzo wrote, directed, and edited six episodes of a new docu-fiction set inside the Sala Rossa (emergency intensive care unit) of the Umberto I Hospital in Rome. Sala Rossa won a special mention from critics at the Turin Film Festival. In 2001, together with Mario Gianani, he founded the production company Offside, which initially focused on documentaries and historical television programs, before moving into feature films, including Private (2004), his directorial debut. Presented at the Locarno International Film Festival, where it was met with critical acclaim, the film won the Golden Leopard, the Best Actor Award, and the Ecumenical Jury Prize. Among other honors, Costanzo also received the Silver Ribbon and David di Donatello awards for Best New Director. Private was sold in over 25 countries.

In the summer of 2006, he directed his second feature film, In Memory Of Myself, based on the novel Lacrime impure (also known as The Perfect Jesuit) by Furio Monicelli, shot on the island of San Giorgio Maggiore in Venice. The film was presented in competition at the Berlinale in 2007. In the previous year, he also directed the documentary Auschwitz 2006, presented in the Extra section of the Rome Film Festival. The story depicts an educational trip to the Auschwitz concentration camp, organized by Mayor Walter Veltroni and the Jewish community of Rome, for a group of 250 high school students.

2010 marked his third feature film, The Solitude of Prime Numbers, based on the bestselling novel by Paolo Giordano, which sold over two million copies in Italy and was translated into more than thirty languages. The film, in competition at the 67th Venice International Film Festival, which starred Luca Marinelli and Alba Rohrwacher, earned the Pasinetti Award, the Silver Ribbon, and the Globo d’Oro for Best Actress. In 2014, he directed Hungry Hearts, based on Marco Franzoso’s novel Il bambino indaco, starring Alba Rohrwacher and Adam Driver. The film was presented in competition at the Venice Film Festival, where both lead actors received the Volpi Cup for their performances. Costanzo then directed the first, second, and third seasons of In Treatment for Sky Cinema, the Italian adaptation of the HBO series based on the original Israeli format created by Hagai Levi. Sergio Castellitto played the part of the psychotherapist Giovanni Mari.

In 2018 and 2020, he wrote and directed the first and second seasons of the Rai-HBO series My Brilliant Friend, based on Elena Ferrante’s acclaimed Neapolitan Novels, also co-writing the screenplays for the third and fourth seasons. Premiering in Venice with its first two episodes, the series aired on HBO in the United States and Rai in Italy, later sold in more than 160 countries.

In 2023, Costanzo presented Finally Dawn in competition at the Venice Film Festival. Written by Costanzo himself, the film draws inspiration from the infamous Montesi murder case, telling the story of a simple young woman—a very young extra at Cinecittà in 1950s Rome—who accepts a glamorous invitation from a group of American actors and spends an endless night with them. The film stars Lily James, Alba Rohrwacher, and Willem Dafoe, and earned its lead actress, Rebecca Antonaci, the Biraghi Award at the Silver Ribbons and the Globo d’Oro for Best Emerging Talent, as well as the Silven Ribbons for Best Production Design and Best Costume Design.