After finishing school in 1950, Wilms began studying economics, social policy and sociology in Cologne, graduating in 1954.
In 1956, she received a PhD completing a study on the macro and micro-economic processes in the German economy.
From 1953 to 1973 she worked as a research assistant for youth and vocational training at the Institute of German Economy in Cologne.
Wilms was appointed on 4 October 1982 as the Federal Minister for Education and Science in the Cabinet of Chancellor Helmut Kohl.
Since 1992 she was the chairperson of the Board of Trustees of the Public Service Foundation Chancellor Adenauer-Haus in Bad Honnef.