Andrew Tsubaki was born to Ken and Yasu Tsubaki in Tokyo, Japan in 1931. In 1954, Tsubaki received a bachelor of arts degree in English from Tokyo Gakugei University. He would go on to earn a post-graduate degree in drama from the University of Saskatchewan in 1959, a Master's of Fine Arts in theatre arts from Texas Christian University in 1961, and a doctorate in speech and drama from the University of Illinois Champaign-Urbana in 1967 with his thesis, "Zeami and the Transition of the Concept of Yugen: A Note on Japanese Aesthetics." Throughout his career, Tsubaki was a strong advocate for Japanese traditional theatre, particularly the kabuki and noh styles, and in 2007, he was awarded the 'Order of Japan' by the Japanese government for his life's work in promoting cultural exchange between Japan and the United States.

Tsubaki was a teacher at the Bunkyo-ku 4th Junior High School in Tokyo from 1954 to 1958 before moving to Canada and then the United States. He became a naturalized citizen of the United States in 1973. Tsubaki worked as a design instructor and technical director at Bowling Green State University from 1964 to 1968 before becoming an assistant professor at the University of Kansas (KU). During his time at KU from 1968-2000, Tsubaki went on to become an associate professor and then professor in the Theatre and Film Department, as well as teaching and serving in the East Asian Languages and Cultures Department.

While at KU, Tsubaki served as the director of the International Theatre Studies Center from 1971 to 2000 and the director of International Classical Theatre in 1988. From 1983-1990, he was also the chair of the Department of East Asian Languages and Cultures. In 2000, Tsubaki retired and became professor emeritus.

Tsubaki directed many plays, including Kanjincho, Rashomon, King Lear, Fujito, Shimizu, Hippolytus, Busu, The Missing Lamb, Suehirogari, Sumidagawa, and Tea between 1973-1995. Tsubaki also choreographed the following plays: Hamlet, The Resistible Rise of Arturo Ui, Man and the Masses, The Children of Fate, and The Great Theatre of the World from 1987 to 1994.

Tsubaki was a visiting professor and guest lecturer at many institutions, including Carleton College in 1974 and 1993, Tsuda University and Tel-Aviv University in 1975, Missouri Repertory Theatre in 1976, and the National School of Drama at New Delhi, India in 1983. He served with several academic organizations, including the College of American Theatre, the American Theatre Association, the Asian Theatre Program, Association for Asian Studies, Association for Kansas Theatres, Association for Theatre in Higher Education, and the Association for Asian Performance. Tsubaki also served as an editor or contributing author for the following publications: Asian Theatre Journal from 1982 to 1994, Studies in American Drama from 1985-1988, Theatre Companies of the World in 1986, Indian Theatre: Traditions of Performance in 1990, and International Dictionary of Theatre in 1992 and 1994.

With his professional career, Tsubaki also studied aikido and helped to reform the Kansas Ki Society before eventually becoming the Sensei of the Kansas Ki Society. In 1987, Tsubaki began teaching aikido courses at KU and helped to expand the academic program in the 1990s to bring KU students to train with Koichi Tohei Sensei at the Ki Society Headquarters in Japan. Through his leadership, the Kansas Ki Society became one of the largest schools in the Midland Ki Federation. Tsubaki passed away in 2009.

Tsubaki married Lilly Yuri Takashiba in 1963, and they had two sons, Arthur Yuichi and Phillip Takeshi.