Schwartz was born and raised in Brooklyn, New York. His parents, Harry and Rose, separated when Schwartz was nine, and their divorce had a profound effect on him. Later, in 1930, another traumatizing event occurred when Schwartz's father suddenly died at the age of 49. Though Harry had accumulated a good deal of wealth from his dealings in the real estate business, Delmore only inherited a few thousand dollars due to the shady dealings of the dishonest executor of Harry's estate. According to Schwartz's biographer, James Atlas, "Delmore continued to hope that he would eventually receive his legacy [even] as late as 1946".

Schwartz spent time at Columbia University and the University of Wisconsin before finally graduating from New York University in 1935. He then went on to do some graduate work in philosophy at Harvard University where he studied with the philosopher Alfred North Whitehead, but Schwartz left without receiving a degree and returned to New York. Soon thereafter, he made his parents' disastrous marriage the subject of his most famous short story, "In Dreams Begin Responsibilities" which was published in 1937 in the first issue of Partisan Review. This story and other short stories and poems were collected and released in his first book, also entitled In Dreams Begin Responsibilities, in 1938. The book was well received, and made him a well-known figure in New York intellectual circles. His work received praise from some of the most respected people in literature, and he was considered one of the most gifted writers of his generation.

In 1937, he also married his first wife, a book reviewer for Partisan Review, Gertrude Buckman, whom he divorced after six years.

For the next couple of decades, he continued to publish stories, poems and plays, and edited the Partisan Review from 1943 to 1955 as well as The New Republic. In 1948, he married the much younger novelist, Elizabeth Pollett. This relationship also ended in divorce.

In 1959, he became the youngest-ever recipient of the Bollingen Prize, awarded for a collection of poetry he published that year, Summer Knowledge: New and Selected Poems. His poetry differed in many respects from his stories in that it was not especially autobiographical and was much more philosophical. His verse would also become increasingly abstract in his later years. He taught creative writing at six different universities, including Syracuse, Princeton, and Kenyon College.

In addition to being known as a gifted writer, Schwartz was considered a great conversationalist and spent much time entertaining friends at the White Horse Tavern in New York City.

Much of Schwartz's work is notable for its philosophical and deeply meditative nature, and the literary critic, R.W. Flint, wrote that Schwartz's stories were, "the definitive portrait of the Jewish middle class in New York during the Depression."

He was unable to repeat or build on his early successes later in life as a result of alcoholism and mental illness, and his last years were spent in reclusion at the Columbia Hotel in New York City. In fact, Schwartz was so isolated from the rest of the world that when he died on July 11, 1966 at age 52, of a heart attack, two days passed before his body was identified at the morgue.

Schwartz was interred at Cedar Park Cemetery, in Emerson, New Jersey.

A selection of his short-stories was published posthumously in 1978 under the title In Dreams Begin Responsibilities and Other Stories and was edited by James Atlas who had just written a biography on Schwartz, Delmore Schwartz: The Life of An American Poet, two years prior. Later, another collection of Schwartz's work, Screeno: Stories & Poems, was published in 2004. This collection contained fewer stories than In Dreams Begin Responsibilities and Other Stories but it also included a brief selection of some of Schwartz's best-known poems like "The Heavy Bear Who Goes With Me" and "In The Naked Bed, In Plato's Cave." Screeno also featured an introduction by the fiction writer and essayist Cynthia Ozick.

One of the earliest, well-known tributes to Schwartz came from Schwartz's friend, fellow-poet, Robert Lowell, who published the poem "To Delmore Schwartz" in 1959 (while Schwartz was still alive) in the book Life Studies. In "To Delmore Schwartz," Lowell reminisces about the time that the two poets spent together at Harvard in 1946, writing that they were "underseas fellows, nobly mad,/ we talked away our friends."

One year following Schwartz's death, in 1967, his former student at Syracuse University, the rock musician Lou Reed dedicated his song "European Son" to Schwartz (although the lyrics themselves made no direct reference to Schwartz).

Then, in 1968, Schwartz's friend and peer, fellow-poet John Berryman dedicated his book His Toy, His Dream, His Rest "to the sacred memory of Delmore Schwartz" including 12 elegiac poems about Schwartz in the book. In "Dream Song #149," Berryman wrote of Schwartz,

In the brightness of his promise,unstained, I saw him thro' the mist of the actualblazing with insight, warm with gossipthro' all our Harvard yearswhen both of us were just becoming knownI got him out of a police-station once, in Washington, the world is trefand grief too astray for tears.

The most ambitious literary tribute to Schwartz came in 1975 when Saul Bellow, a one-time protege of Schwartz's, published his Pulitzer Prize-winning novel Humboldt's Gift which was based on his relationship with Schwartz. Although the character of Von Humboldt Fleischer is Bellow's portrait of Schwartz during Schwartz's declining years, the book is actually a testament to Schwartz's lasting artistic influence on Bellow.

Lou Reed's 1982 album The Blue Mask included Reed's second Schwartz homage with the song "My House." This song is much more of a tribute to Schwartz than the above-mentioned "European Son" since the lyrics of "My House" are actually about Reed's relationship with Schwartz. In the song, Reed writes that Schwartz "was the first great man that I ever met."

In 2009 New York-based recording artist Mark Donato released "A History of the Boys and Girls," the title of which was inspired by Schwartz' unfinished, unpublished novel "A History of the Boys and the Girls." Donato left out the second "the" for continuity.

• In Dreams Begin Responsibilities (1938), a collection of short stories and poems
• Shenandoah (1941), a verse play
• Genesis (1943), a prose poem about the growth of a human being
• World Is a Wedding (1948), a collection of short stories
• Vaudeville for a Princess and Other Poems (1950)
• Summer Knowledge: New and Selected Poems (1959)
• Successful Love and Other Stories (1961)

Published posthumously:

• Selected Essays (1970, ed. Donald Dike, David Zucker)
• In Dreams Begin Responsibilities and Other Stories (1978, New Directions), a short story collection
• Letters of Delmore Schwartz (1984, ed. Robert Phillips)
• The Ego Is Always at the Wheel: Bagatelles (1986, ed. Robert Phillips), a collection of humorously whimsical short essays
• Last and Lost Poems (1989, ed. New Directions)
• Screeno: Stories & Poems (2004, New Directions)