Stone is the David Morrisroe Professor of Physics at the California Institute of Technology (1994 to date), Vice Provost for Special Projects (2004 to date), and formerly the Director of the Jet Propulsion Laboratory (1991-2001). As Vice Provost for Special Projects, he has served as either Chair or Vice Chair of the Board of Directors of the TMT Observatory Corporation that oversees the design development of the Thirty Meter Telescope (TMT) on behalf of Caltech, the University of California, and the Association of Canadian Universities for Research in Astronomy (ACURA), joined by the National Astronomical Observatory of Japan, the National Astronomical Observatories of the Chinese Academy of Sciences, and the Department of Science and Technology of India.

Stone earned his Associate of Arts degree in 1956 from Burlington Junior College and his M.S. (1959) and Ph.D. (1964) degrees in physics from the University of Chicago. He joined the Caltech faculty in 1964 as a research fellow in physics, jointly establishing the Space Radiation Laboratory and has served as Chair of the Division of Physics, Mathematics, and Astronomy (1983-1988) and as Vice President for Astronomical Facilities (1988-1990).

Since 1972, Stone has also served as the Chief Scientist for the Voyager Mission at the Jet Propulsion Laboratory. Following the launch of the twin Voyager spacecraft in 1977, he coordinated efforts of eleven teams of scientists in their studies of Jupiter, Saturn, Uranus, and Neptune. He continues to coordinate five teams of scientists as the Voyager spacecrafts continue to explore.

Stone has been principal investigator on nine NASA spacecraft and a co-investigator on five other NASA missions. He has served as the project scientist for the Voyager Mission since 1972, coordinating the studies of Jupiter, Saturn, Uranus, and Neptune and the continuing search for the edge of interstellar space.

From 1985 to 2009, he was a member of the Board of Directors of the California Association for Research in Astronomy (CARA), which is responsible for building and operating the W. M. Keck Observatory with its two ten-meter telescopes on Mauna Kea, Hawaii. As either Chair or Vice Chair of the Cara Board, he had oversight responsibility for the observatory and led the funding development for the second telescope.

Stone is a member of the National Academy of Sciences, the American Philosophical Society, and the International Academy of Astronautics, a fellow of the American Physical Society, the American Geophysical Union, the American Institute of Aeronautics and Astronautics, the Royal Aeronautical Society, and the California Council on Science and Technology, and a member of the American Astronomical Society.

Among his awards is the National Medal of Science (1991), the Magellanic Award from the American Philosophical Society, the IAF Alan D. Emil Award, and the IAA von Karman Award. He has received two NASA Exceptional Scientific Achievement Medals, three NASA Distinguished Service Medals, the NASA Distinguished Public Service Medal, and two NASA Outstanding Leadership Medals. He has also received the Dryden Medal, the Space Science Award, and the von Karman Lectureship in Astronautics from the American Institute of Aeronautics and Astronautics, the Aviation Week & Space Technology Aerospace Laurels Award, the National Space Club Science Award, the American Academy of Achievement Golden Plate Award, the COSPAR Award for Outstanding Contributions to Space Science, the International von Kármán Wings Award, and the Carl Sagan Award and the Space Flight Award from the American Astronautical Society. He has been inducted into the Aviation Week & Space Technology Hall of Fame and was a Sloan Foundation Fellow, and honorary degrees from Washington University in St. Louis, Harvard University, the University of Chicago, and the University of Southern California. In 1996 asteroid (5841) was named after him.