J.R.R. Tolkien published the final volume of The Lord of the Rings, The Return of the King, in the United Kingdom in 1955. Allen & Unwin issued it on 20 October 1955.
The first volume, The Fellowship of the Ring, appeared in 1954, followed by The Two Towers later that year. The trilogy’s final volume contains the conclusion of the War of the Ring and extensive appendices about languages, calendars, family histories, and chronology.
Tolkien preferred the title The War of the Ring because he thought The Return of the King revealed too much about the story. His publisher retained the more marketable title, which refers primarily to Aragorn’s return to his rightful kingship.
American publication followed in 1956 through Houghton Mifflin. This difference explains why some references give 1955 and others mention 1956 when discussing the trilogy’s completion. The question’s date refers specifically to the original United Kingdom edition.