Rosenbaum is currently the provost and John T. Wilson Distinguished Service Professor of Physics at the University of Chicago.
Caltech said Thursday that the 58-year-old Rosenbaum will succeed Jean-Lou Chameau, who served as president from 2006 to 2013.
Rosenbaum is an expert on condensed matter physics. He received his bachelor's degree in physics from Harvard University and both a master's degree and doctorate in physics from Princeton University.
Rosenbaum will take over at Caltech on July 1, 2014, from interim president and provost Edward Stolper.
Rosenbaum's spouse, Katherine T. Faber, will join the Caltech faculty. She's currently the Walter P. Murphy Professor of Materials Science and Engineering at Northwestern University.