Born in Lausanne, Switzerland, Radziwill was the son of socialite/actress Caroline Lee Bouvier (younger sister of First Lady Jacqueline Lee Bouvier) and Polish Prince Stanisław Albrecht Radziwiłł. He married a former ABC colleague, Emmy Award-winning journalist Carole Ann DiFalco, on 27 August 1994 on Long Island, New York.
As a member of the Radziwills, one of Central Europe's noble families, Anthony Radziwill was customarily accorded the title of Prince and styled His Serene Highness, although he never used it. The family's vast hereditary fortune was lost during World War II, and Anthony's branch of the family immigrated to the United Kingdom, where they became British subjects.
Anthony Radziwill was raised Roman Catholic there; he attended Colet Court preparatory school in London, and later Choate Rosemary Hall preparatory school in Wallingford, Connecticut, graduating in 1978. In 1982, he finished his studies at Boston University, earning a bachelor's degree in broadcast journalism.
Radziwill's career began at NBC Sports, as an associate producer. During the 1988 Winter Olympics in Calgary, Alberta, Canada, he contributed Emmy Award-winning work. In 1989, he joined ABC News as a television producer for Prime Time Live. In 1990, he won the Peabody Award for an investigation on the resurgence of Nazism in the United States. Posthumously, Cancer: Evolution to Revolution was awarded a Peabody. His work was nominated for two Emmys.
Around 1989 he was diagnosed with testicular cancer and underwent treatment which left him sterile, but in apparent remission. However, shortly before his wedding, new tumors emerged. Radziwill battled metastasizing cancer throughout his five years of marriage, with his wife serving as his primary caretaker through a succession of oncologists, hospitals, operations, and experimental treatments.
The couple lived in New York, and both Radziwill and his wife tried to maintain their careers as journalists between his bouts of hospitalization. During this period, Radziwill became especially close to his maternal aunt Jacqueline Kennedy Onassis, who was also terminally ill with cancer.
On September 21, 1996, Radziwill was the best man for the wedding of his best friend and cousin John F. Kennedy Jr. (Jacqueline's son) and Carolyn Bessette. John Jr.'s older sister, Caroline Kennedy Schlossberg, was the matron of honor.
Radziwill died on 10 August 1999, nearly a month after John Jr. and Carolyn Bessette perished in a plane crash on July 16, 1999. Radziwill, who was cremated, was survived by his sister, Anna Christina Radziwill (who was born in 1960, married Ottavio Arancio in September 1999, and divorced in 2005) and his elder half-brother, Jan Stanislas Radziwill (who was born in 1947 of their father's second marriage to Grace Kolin, and is the father of two sons, Jan Michal (born 1979), and Filip (born 1981), by his wife Eugenia Carras).
In 2000, his mother, Lee Radziwill, and widow, Carole Radziwill, set up a fund to help emerging documentary filmmakers. In 2005, Carole wrote an autobiography, focused largely on her marriage to Radziwill. Titled, What Remains: A Memoir of Fate, Friendship and Love (Scribner), the book made the New York Times Best Seller List.