Kopper was born in Oslanin (Osłonino, Poland) to a Mennonite family, he was expelled after World War II Since 2003, he is married to Brigitte Seebacher-Brandt, the third wife of Willy Brandt. One of his three children of his first marriage is the historian Christopher Kopper.
Kopper was employed as a trainee in Deutsche Bank in 1954 and spent his whole career there. He became a board member in 1977, and after the terrorist murder of Alfred Herrhausen in 1989, he became chairman. He chaired the supervisory board of DaimlerChrysler from 1998 to 2007. He is a former member of the Steering Committee of the Bilderberg Group. He is also a jury member of the Franz Werfel Human Rights Award.
Kopper received widespread public and media attention in 1994, when he used the word "peanuts" to describe a sum of DM 50 million. A jury of linguistic scholars subsequently voted the term as German Un-Word of Year, thus criticizing the widely differing definitions of a non-notable amount of money by bank managers and average people.
- Die Bank lebt nicht vom Geld allein. Beiträge zu Kultur und Gesellschaft 1994–1997. herausgegeben von Brigitte Seebacher-Brandt, Piper Verlag, München 1997, 144 S., ISBN 3-492-22584-5.
- "Mr. Peanuts" hängt an der Macht vom 10. März 2005 auf Spiegel Online
- "Former Steering Committee Members". bilderbergmeetings.org. Bilderberg Group. Retrieved 2014-02-08.
- Spiegel Online: Ein Jahr, ein (Un-)Wort! (in German).