The poem, which has been called "arguably the best-known verses ever written by an American", is largely responsible for the conception of Santa Claus from the mid-nineteenth century to today, including his physical appearance, the night of his visit, his mode of transportation, the number and names of his reindeer, as well as the tradition that he brings toys to children. Prior to the poem, American ideas about St. Nicholas and other Christmastide visitors varied considerably. The poem has influenced ideas about St. Nicholas and Santa Claus beyond the United States to the rest of the English-speaking world and beyond. According to legend, A Visit was composed by Moore on a snowy winter's day during a shopping trip on a sleigh. His inspiration for the character of Saint Nicholas was a local Dutch handyman as well as the historical Saint Nicholas. While Moore originated many of the features that are still associated with Santa Claus today, he borrowed other aspects such as the names of the reindeer. The poem was first published anonymously in the Troy, New York, Sentinel on December 23, 1823, having been sent there by a friend of Clement Clarke Moore, and was reprinted frequently thereafter with no name attached. Only later did Moore acknowledge his authorship, and the poem was included in an 1844 anthology of his works. Moore had written it for his children, and being a scholar and professor, did not wish at first to be connected with the poem, but his children insisted that it be included in the anthology.

Moore's conception of St. Nicholas was borrowed from his friend Washington Irving's, but Moore portrayed his "jolly old elf" as arriving on Christmas Eve rather than Christmas Day. At the time Moore wrote the poem, Christmas Day was overtaking New Year's Day as the preferred genteel family holiday of the season, but some Protestants - who saw Christmas as the result of "Catholic ignorance and deception" - still had reservations. By having St. Nicholas arrive the night before, Moore "deftly shifted the focus away from Christmas Day with its still-problematic religious associations". As a result, "New Yorkers embraced Moore's child-centered version of Christmas as if they had been doing it all their lives"

In An American Anthology, 1787–1900, editor Edmund Clarence Stedman reprinted the Moore version of the poem, including the German spelling of "Donder and Blitzen" he adopted, rather than the earlier Dutch version from 1823, "Dunder and Blixem". Both phrases translate as "Thunder and Lightning" in English, though the German word for thunder is "Donner", and the words in modern Dutch would be "Donder en Bliksem".

Modern printings frequently incorporate alterations that reflect changing linguistic and cultural sensibilities: For example, breast in "The moon on the breast of the new-fallen snow" is frequently bowdlerized to crest, the archaic ere in "But I heard him exclaim ere he drove out of sight" is frequently replaced with as, and "Happy Christmas to all, and to all a good-night" is frequently rendered with the modern North American locution "'Merry Christmas'" and with "goodnight" as a single word.