Krige is originally a physical chemist by training, earning a PhD from the University of Pretoria in the subject. After earning a PhD in philosophy at the University of Sussex, in the United Kingdom in 1979, Krige's intellectual career has been in the history of science and technology, including notable efforts within the project to write the history of CERN and the European Space Agency in the 1980s and 1990s. His main focus is on the place of science and technology in the foreign policies of governments both intra-European and between the U.S. and Western Europe in the cold war.
In 2000, Krige became a professor at Georgia Institute of Technology's School of History and Sociology.
As a Francis Bacon Award recipient, Krige became a visiting professor at Caltech's Division of Humanities and Social Science.