University spokeswoman Tracey Reeves said Muller died of respiratory failure. His wife, Jill McGovern, was at his side.
Muller had been provost of Johns Hopkins for 10 months when was tapped by trustees in 1972 to lead the Baltimore-based university, staying at the helm until 1990. He also served as hospital president from 1972 to 1983.
University officials said Muller led highly successful fundraising campaigns that raised hundreds of millions of dollars for Hopkins. Under Muller, the university broke off nursing and engineering studies into standalone schools, brought the Space Telescope Science Institute to Baltimore, and established the Johns Hopkins-Nanjing University Center for Chinese and American Studies.
Muller also created an affiliation with the Peabody Institute, helping put the well-known music school on stronger financial footing, and helped to restore and reopen the Homewood Museum and Evergreen Museum and Library.
He also presided over the expansion and modernization of Johns Hopkins Bayview Medical Center and the establishment of the Krieger Mind-Brain Institute.
University president Ronald J. Daniels praised Muller as "a remarkable leader whose vision and determination enhanced dramatically the institution's national and global prominence."
"A man of both substance and impeccable style, Dr. Muller is credited with moving the university into a new era while preserving its tradition of leadership among research institutions," Daniels wrote in an email to the university community. "As many of you who knew him can attest, he was a no-nonsense leader who was more formal than informal. More bold than quiet. More personable than pushy."
Born in Hamburg, Germany, Muller was a child when his family fled Nazi Germany. He spent his teenage years in Los Angeles, even acting in several Hollywood movies before enrolling at the University of California, Los Angeles, from which he graduated in 1948. He earned a degree in politics from Oxford University, where he was a Rhodes Scholar, and received a doctorate from Cornell University. Before his tenure at Hopkins, Muller served as a vice president of public affairs at Cornell and as director of its Center for International Studies.
After his retirement. Muller remained active in the Hopkins community and was awarded an honorary doctorate of humane letters in 2000.