Alexander was born in Philadelphia, Pennsylvania, in 1924 and grew up in the suburb of Drexel Hill. His father was a stockbroker, and their family was greatly affected by the Great Depression. According to Alexander, his parents didn't read books and only bought them from the Salvation Army "to fill up empty shelves."

Alexander graduated in 1940 from Upper Darby High School, where he was inducted into the school's Wall of Fame in 1995. He decided he wanted to be a writer at age 15, but his parents were so upset that they placed him at Haverford College just down the road from home (although he left after completing only a single term). Looking for adventure, he served during World War II in the US Army, where he rose to be a staff sergeant in intelligence and counterintelligence after he trained in Wales, which would become the setting of many of his books. Alexander then attended the University of Paris, where he met Janine Denni. They were married in 1946.

Alexander died on May 17, 2007, two weeks after the death of his wife of sixty-one years. He is buried at Arlington Cemetery Co in Drexel Hill, Pennsylvania. His daughter, Madeleine Khalil, died in 1990.

Alexander's most well-known novels are within the genre of children's literature, with The Chronicles of Prydain being his most famous work. The five-volume series of children's fantasy novels detail the adventures of a young man named Taran, who is awarded the honor of Assistant Pig-Keeper but dreams of being a grand hero, and his companions Princess Eilonwy, Fflewddur Fflam the wandering bard and king, a feral yet gentle creature called Gurgi, and a dwarf named Doli. The book focuses on Taran's progression from youth to maturity, with the series being loosely inspired by Welsh mythology and the Mabinogion. The first two books in this series formed the basis of the Disney animated film The Black Cauldron.

Alexander's other major fiction series are the Westmark trilogy, about a printer's apprentice involved in political intrigue in a faux-European kingdom, and the Vesper Holly series, about a wealthy and brilliant Philadelphia orphan who has adventures in various fictional 19th century countries. His picture book The Fortune Tellers (1992), illustrated by Trina Schart Hyman, created something of a controversy because some felt that the story was of European origin and thus contextually inappropriate for the book's African setting.

Alexander's last novel, The Golden Dream of Carlo Chuchio, was published in August 2007. "I have finished my life work," Alexander said about the book before he died.The Dictionary of Literary Biography said Alexander's books had "the special depth and insight provided by characters who not only act, but think, feel and struggle with the same kinds of problems that confuse and trouble people in the twentieth century."

In describing the influences on his writing, Alexander once said, "Shakespeare, Dickens, Mark Twain and so many others were my dearest friends and greatest teachers. I loved all the world's mythologies: King Arthur was one of my heroes."

Alexander began to receive significant critical acclaim with the release of his Chronicles of Prydain series. The second book, The Black Cauldron, was a 1966 Newbery Honor book. The fourth book in the series, Taran Wanderer, was a School Library Journal Best Book of the Year. The fifth and final book in the series, The High King won the 1969 Newbery Medal and was a finalist for both the National Book Award and the American Book Award. However, Alexander's other books were praised as well. "The Marvelous Misadventures of Sebastian," won a 1971 National Book Award. He also won a 1982 National Book Award (at that time temporarily known as the American Book Award) for Westmark.

Among his other awards were the Boston Globe-Horn Book Award for The Fortune-Tellers. In 1972 he was included in the prestigious reference series, Book of Junior Authors and Illustrators.

On January 28, 2010 an exhibit opened at the Harold B. Lee Library on the campus of Brigham Young University, displaying several items from Alexander's home office, which he referred to as "the Box." Items include manuscripts, editions of all his books, his violin, typewriter, and desk.

The Chronicles of Prydain

* The Book of Three (1964)

* The Black Cauldron (1965) - Winner of the 1966 Newbery Honor

* The Castle of Llyr (1966)

* Taran Wanderer (1967)

* The High King (1968) - Winner of the 1969 Newbery Medal

* The Foundling and Other Tales from Prydain (1970)

The Westmark Trilogy

* Westmark (1981)

* The Kestrel (1982)

* The Beggar Queen (1984)

The Vesper Holly series

* The Illyrian Adventure (1986)

* The El Dorado Adventure (1987)

* The Drackenberg Adventure (1988)

* The Jedera Adventure (1989)

* The Philadelphia Adventure (1990)

* The Xanadu Adventure (2005)

Other

* And Let the Credit Go (1955) (first published book)

* My Five Tigers (1956)

* August Bondi: Border Hawk (1958)

* Janine (my wife, that is) is French (1960)

* Aaron Lopez: The Flagship Hope (1960)

* Fifty Years in the Doghouse (1963)

* The Remarkable Journeys of Jason And Gareth (1963)

* The Truthful Harp (1967)

* The Marvelous Misadventures of Sebastian (1970)

* The King's Fountain (1971)

* The Four Donkeys (1972)

* The Cat Who Wished to Be a Man (1973)

* The Wizard in the Tree (1974)

* The Town Cats and Other Tales (1977)

* The First Two Lives of Lukas-Kasha (1978)

* The Remarkable Journey of Prince Jen (1991)

* The Fortune-Tellers (1992)

* The Arkadians (1995)

* The House Gobbaleen (1995)

* The Iron Ring (1997)

* Gypsy Rizka (1999)

* How the Cat Swallowed Thunder (2000)

* The Gawgon and the Boy (2001) (UK title The Fantastical Adventures of the Invisible Boy)

* The Rope Trick (2002)

* Dream-of-Jade: The Emperor's Cat (2005)

* The Golden Dream of Carlo Chuchio (2007)

Translations

* "The Diary of Antoine Roquentin" (John Lehmann, 1949). This was the first English translation of the celebrated existentialist novel "La Nausée" by Jean-Paul Sartre (Gallimard 1938).