Sverdrup he joined the U.S. Army in 1918 as a private. He left the service after World War I to receive a bachelor of arts degree from Augsburg College and a bachelor of science degree in civil engineering from the University of Minnesota. Sverdrup returned to the military during World War II when he served as a colonel in the Corps of Engineers. In 1945 he was promoted to major general and put in charge of the Engineering Construction Command for the Pacific Theater of War. He received the Distinguished Service Cross and was honored by Gen. Douglas MacArthur as "the engineer soldier at his best."

Sverdrup´s firm opened its doors as Sverdrup & Parcel in 1928 as a partnership between Sverdrup and his college engineering professor, John I. Parcel. For the first 10 years of its existence, the firm concentrated its efforts almost entirely on bridge building. Today it is one of the world´s largest companies in engineering, architecture and construction, having merged with Jacobs Engineering Group in January 1999. Sverdrup also served the St. Louis area through his community involvement. He was instrumental in bringing the black community together, worked endless hours with the Boy Scouts, and was the first chairman of the Bi-State Development Commission.