Roberts grew up in the The Bronx, New York City. At age 15, she abandoned her studies to get married and lived for a while hitch-hiking across the United States until her mother-in-law annulled the union. Roberts continued to live in New York City, modeling and working as a dance teacher with Arthur Murray. After meeting psychology student Barry Roberts while waiting in line for a movie, she soon married again, having proposed to him in a subway station. While Barry started a career as a screenwriter, Tanya began to study at the Actors Studio with Lee Strasberg and Uta Hagen. She appeared in off-Broadway productions of "Picnic" and "Antigone" and in television commercials for Ultra Brite, Clairol and Cool Ray sunglasses.

In 1977 Tanya and her husband moved to Hollywood. She began appearing in such made-for-TV films as “Pleasure Cove,” “Zuma Beach,” & “Waikiki.” Her film debut was in “Forced Entry.” After appearing in several minor films, her first big break came when she was selected as an angel (the last) for "Charlie's Angels" in its final season, and was featured on the cover of "People" magazine. The attention she garnered as the newest Charlie's Angel helped secure her most significant film parts “The Beastmaster,” the title role in “Sheena” & as a Bond girl in “A View to a Kill.”

Roberts can currently be heard on commercials for a wide variety of radio stations and programs for Consolidated Resorts.