After gaining his Diplom in physics and working at IBM, Tschira co-founded the German software giant SAP AG in 1972 in Mannheim, Germany together with Hans-Werner Hector, Dietmar Hopp, Hasso Plattner and Claus Wellenreuther. From 1998 to 2007, he was a board member at SAP. He was married to Gerda Tschira and had two sons, Harald and Udo.
The Klaus Tschira Foundation (KTF) was established by Tschira in 1995 as a non-profit organization. Its primary objective is to support projects in natural and computer sciences as well as mathematics. The KTF places strong emphasis on public understanding in these fields. Tschira's commitment to this objective was honored in 1999 with the "Deutscher Stifterpreis" by the German National Academic Foundation (German: Studienstiftung). The KTF is located at the Villa Bosch in Heidelberg, Germany, the former residence of Nobel Prize laureate for chemistry Carl Bosch (1874–1940).
In 2008, Tschira and his wife Gerda founded the Gerda and Klaus Tschira Foundation.