Born Nelson Ahlgren Abraham in Detroit, Michigan, Algren moved to Chicago, Illinois with his parents at the age of three to live in a working-class, immigrant neighborhood on the South Side. His father was the son of a Swedish convert to Judaism and a Jewish American woman, while his mother (who owned a candy store) was of German Jewish descent. When Algren was eight years old, his parents moved from the far south side neighborhood of St. Columbanus to the north side, living in an apartment on North Troy Street while his father worked as an auto mechanic on North Kedzie Avenue.

Algren was educated in Chicago's public schools, graduated from Roosevelt High School, and went on to study at the University of Illinois at Urbana-Champaign, graduating with a Bachelor of Science in journalism during the Great Depression in 1931. He wrote his first story, "So Help Me," in 1933, while he was in Texas working at a gas station. Before returning home, he was caught stealing a typewriter from an abandoned classroom. For this, he spent a month behind bars and faced a possible three additional years in jail. Fortunately for him, Algren was released, but the incident made a deep impression on him. It deepened his identification with outsiders, has-beens, and the general failures who later populated his fictional world.

His first novel, Somebody in Boots, was published in 1935. Never Come Morning, published in 1942, portrayed the dead-end life of a doomed young criminal.

He served as a private in the European Theater of WWII, as a litter bearer. Despite being a college graduate, he was denied entry into Officer Candidate School. There is conjecture that this may have been due to suspicion regarding Algren's political beliefs.

He articulated the world of "drunks, pimps, prostitutes, freaks, drug addicts, prize fighters, corrupt politicians, and hoodlums". He is probably best known for his 1950 National Book Award winning The Man with the Golden Arm. His next book, Chicago, City on the Make (1951) was a scathing essay that outraged the city's boosters but beautifully presented the back alleys of the town, its dispossessed, its corrupt politicians and its swindlers. Nonconformity, published in 1994, presents Algren's side of the debacle which was the 1956 film adaptation of "Golden Arm." Nonconformity also expresses the belief system behind Algren's writing not to mention a call to writers everywhere to investigate the dark and represent the ignored.

Algren had a storied affair with Simone de Beauvoir and they travelled to Latin America together in 1949. In her novel The Mandarins (1957), she wrote of Algren (who is "Lewis Brogan" in the book):

"At first I found it amusing meeting in the flesh that classic American species: self-made leftist writer. Now, I began taking an interest in Brogan. Through his stories, you got the feeling that he claimed no rights to life and that nevertheless he had always had a passionate desire to live. I liked that mixture of modesty and eagerness." According to Herbert Mitgang, the US Federal Bureau of Investigation did not like Algren's political views and kept a dossier on him amounting to more than 500 pages, but identified nothing concretely subversive. (Mitgang, Dangerous Dossiers: Exposing the Secret War Against America's Greatest Authors, NY: Donald I. Fine, Inc. 1988.)

It is generally accepted that Algren wrote best about his beloved Chicago. His last Chicago residence was a walk-up apartment on the north side of west Evergreen Street, just east of Damen Avenue, in a neighborhood that was once one of Chicago's toughest and most crowded Polish slums, but is now a gentrified, popular nightlife district.

In the 2001 documentary Classic Albums: Lou Reed: Transformer, musician Lou Reed says that Algren's 1956 novel, A Walk on the Wild Side, was the launching off point for his song, "Walk on the Wild Side".