He was the child of Árpád Kosztolányi (1859–1926), physics and chemistry professor and headmaster of a school, and Eulália Brenner (1866–1948), who was of French origin.

He started high school in Szabadka but because of a conflict with his teachers he was expelled, and so he graduated as a private student in Szeged.

In 1910, his first volume of poems, The Complaints of a Poor Little Child, brought nationwide success and marked the beginning of a prolific period in which he published a book nearly every year.

Kosztolányi also produced literary translations in Hungarian, such as Shakespeare's Romeo and Juliet, The Winter's Tale, Lewis Carroll's Alice in Wonderland, Thornton Wilder's The Bridge of San Luis Rey, Lord Alfred Douglas' memoirs on Oscar Wilde, and Rudyard Kipling's "If—".

He was the first authentic[clarification needed] translator of Rilke's poetry, and he worked a Hungarian masterpiece after Paul Valéry's Cimetiere Marin.