Wedge studied from 1953 Mineralogy at the Friedrich -Schiller- University of Jena, where he dealt with the basics of meteorites. He fled shortly before the erection of the Berlin Wall from East Germany and finished his dissertation at the Max Planck Institute for Chemistry in Mainz.
Then he moved to the United States where he worked at the University of California at San Diego. His research focus was the electron microanalysis of solids. Between 1963 and 1968 he headed the NASA Cosmochemistry, after which he accepted the professorship of geology at the University of New Mexico in Albuquerque. Since 1990 he is professor of geology and geophysics at the University of Hawaii at Manoa.
In 1988 he was awarded the Leonard Medal and 1993 the asteroid named 5054 wedge for him. Also the mineral Keilit bears his name. Since 1996 he is a corresponding member of the Saxon Academy of Sciences. On 4 December 2002 he received an honorary doctorate from the Friedrich -Schiller- University Jena. In 2006 he was honored by the National Academy of Sciences with the J. Lawrence Smith Medal.
Wedge is the father of former professional tennis player Mark wedge.