Regarded by many as the "father" of industrial design education, he was born in Persia (Iran) as Alexander Jusserand Kostellow. He studied in Paris and the University of Berlin. He came to US in 1916, where he studied painting at the National Academy, the Art Student's League and the Kansas City Art Institute, where he met and married Rowena Reed.

Both came to Pittsburgh in 1929 to teach at Carnegie Institute of Technology, he in painting and she in sculpture. In 1934 Alexander helped Donald Dohner initiate the first degreed ID program at CIT and was by then teaching design. He and his wife left in 1936 for Pratt Institute to join the faculty there under Dohner, then "Supervisor of Industrial Design." In 1938, Kostellow was listed as an "Instructor in Industrial Design." In 1939 he was invited by Dean Boudreau to initiate a curriculum of "Design and Structure", a now-called "foundation" program, using abstract elements, that he felt emulated the Bauhaus, and which, many say, was the "heart and soul" of the program. In 1940 he was named "Supervisor of Design and Structure."

In the 1940s he worked with John Vassos to develop educational programs of industrial design recommended by the Industrial Designers Institute. In 1943 he was listed as "Supervisor and Professor of Design", while Dohner was listed as "Professor of Industrial Design." After Dohner's untimely death on Christmas Eve in 1944, Alexander headed the 3-year program as" Supervisor of Industrial Design and Supervisor of Design and Structure" at Pratt Institute.

In 1952 he created an Experimental Design Laboratory at Pratt, providing company designers office space adjacent to student drafting and shop areas to do experimental work and to lecture and advise students. Participating companies included General Motors, Shell Oil, and Owens-Corning Fiberglas Corporation. This innovation led to Pratt being recognized as the program closest to production realities. By this time, Pratt’s program had been expanded to four-years.

In 1954, Alexander died in Detroit, where he had been engaged in special summer design consultation work for the Styling Division of General Motors, despite ill health. After Kostellow's death, Robert A. Kölli succeeded him at the Design Laboratory as well as Supervisor at Pratt. In 1959 Pratt formally established a Department of Industrial Design and n 1962, Alexander’s wife Rowena was named Chair of the Department, a position she held until 1966.