Böhm was born into a family of architects in Offenbach, Hessen. His father, Dominikus Böhm, was renowned for having built several churches throughout Germany. His grandfather was also an architect. After having graduated from Technical University of Munich in 1946, he studied sculpture at a nearby fine-arts academy. After 1947, Böhm worked for his father until the latter's death in 1955. Böhm later took over the firm. During this period, he also worked with the "Society for the Reconstruction of Cologne" under Rudolf Schwarz. In 1951, he traveled to New York City where he worked for six months in the architectural firm of Cajetan Baumann. During his travels in America, he met two of his greatest inspirations, German architects Ludwig Mies van der Rohe and Walter Gropius.
In the following decades, Böhm constructed many buildings around Germany, including churches, museums, civic centers, office buildings, homes, and apartments. He has been considered to be both an expressionist and post-Bauhaus architect, but he prefers to define himself as an architect who creates "connections" between the past and the future, between the world of ideas and the physical world, between a building and its urban surroundings. In this vein, Böhm always envisions the color, form, and materials of a building in relationship with its setting. His earlier projects were done mostly in molded concrete, but more recently he has begun using more steel and glass in his buildings, due to the technical advancements in both materials. In many of his projects, his concern for urban planning is evident, again showing his concern for "connections".