Primarily trained as an architect, he was one of the first in his profession to use steel for the construction of tall buildings. Cobb was also known to design in different architectural styles, some examples of which remain especially in Chicago, Illinois, where he worked from 1882 on. Born on August 19, 1859 in Brookline, Massachusetts, he studied one year at the Massachusetts Institute of Technology, but enrolled in the Lawrence Scientific School at Harvard University in 1877. He studied there until 1880, and was awarded a degree in architecture in 1881. He briefly worked for the Boston architectural firm of Peabody & Stearns, moving to Chicago after winning the competition to design a building for the Union Club.
Cobb was one of the designers of the World's Columbian Exposition in Chicago, 1892, and in the same year was appointed a special government architect. During the ten years of holding this office, he designed the Federal Building in Chicago and the League Island buildings in Annapolis. The Chicago Opera House, Chicago Athletic Club, Newberry Library, and
the University of Chicago are among the buildings designed by him.
From 1902 on, he lived in New York City, where he died on March 27, 1931.