Within a few years of beginning his professorship at the University of Kansas, he became dean of the medical school and eventually was chosen by the Kansas Board of Regents to be chancellor of the entire university. Because of his successes at KU, UCLA asked him to become their chancellor. In 1960, after his relationship with Kansas Governor George Docking, he accepted the position and relocated to Los Angeles, California. There, he was also appointed to be a professor of medical history.
At UCLA, he dealt with the turbulence of student movements in the 1960s in a progressive manner, and successfully kept the university stable. Moreover, he worked to establish the university as a first-rate institution in its own right, and not simply a branch of the vast University of California system. He expanded the UCLA library system, enlarged the School of Medicine's basic science programs, convinced the regents of the University of California to purchase and maintain a cyclotron for the school, and founded the Jules Stein Eye Institute. In 1968, he resigned his position as chancellor in order to become Chairman and CEO of the Times Mirror Company, remaining in Los Angeles. He continued in this position until 1980, and remained a director of the company until he retired in 1986.
After his retirement, he became a major philanthropist in Los Angeles for the rest of his life. He served on many philanthropic boards, including the Los Angeles County Museum of Art and the Los Angeles Music Center, raising funds and public awareness of the institutions. Murphy passed away from natural causes in Los Angeles in 1994.
The Franklin D. Murphy Sculpture Garden at UCLA, which he founded, still remains a world-famous permanent sculpture exhibition.
At the University of Kansas, both Murphy Hall and the Murphy Art and Architecture Library are named in his honor.