Mr. Wagner was born May 11, 1923, in the Bronx, New York City. He took his bachelor's degree in philosophy from Earlham College in Indiana, and a master's at Smith College.

He began his career in the theatre as an actor and then an artistic director, before becoming an educator. He founded the acting programs at Tulane Ohio and Temple Universities before being courted for a job at UC San Diego in 1972. He stayed for twenty years. The program is today frequently rated as one of the best in the nation. Among its many graduates are Jefferson Mays, Danny Burstein and director Michael Grief.

He also fostered a tight relationship between the school and La Jolla Playhouse, which was revived in 1983 under the artistic directorship of Des McAnuff.

He retired in 1991, but remained in touch with his students and with the local theatre scene. He also contributed financially to the UCSD theatre program he had founded. The university's Arthur Wagner Theatre and Molli and Arthur Wagner Dance Building are named after him. His name also adorns the annual Wagner New Play Festival.

In 2013, he was awarded the Chancellor's Medal by the university. He is survived by his wife, and their son Wayne.