Cobb attended the Massachusetts Institute of Technology and Harvard University. After a short service with Peabody & Stearns in Boston, he moved to Chicago where he engaged in a nationwide practice for many years. He 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' tenure of his office, he designed the Federal Building at Chicago and the League Island buildings at Annapolis. Since 1902 he had resided in New York. He was one of the first to use steel in the construction of tall buildings. The Chicago Opera House, Chicago Athletic Club, Newberry Library, and the University of Chicago are among the buildings designed by him.