Born in Brooklyn, New York, he graduated in 1891 from Columbia University and also studied at the Ecole des Beaux Arts in Paris, France.
He designed more than 225 buildings, bridges, and monuments in the United States. Currently 22 are listed on the National Register of Historic Places. He also practiced independently from a Pittsburgh, Pennsylvania office.
He also helped to establish Carnegie Mellon School of Architecture that same year. He also designed many of the original buildings of Emory University in Atlanta. Among his many landmarks are:
Rodef Shalom Temple, Pittsburgh (1904)
Soldiers and Sailors National Military Museum and Memorial, Pittsburgh (1907)
Pittsburgh City-County Building, (1915–1917, with Edward B Lee)
At his Alma Mater, St. Anthony Hall Fraternity, New York (Building #96000484 listed as "Delta Psi, Alpha Chapter".
Hornbostel is also noted for his work on the Queensboro Bridge (1909), and the Hell Gate Bridge (1916) done jointly with Gustav Lindenthal.
Member, State Art Member: F. and Master of Arts. Independent Order of Odd Fellows. Junior. Order of United American Mechanics.
Benevolent and Protective Order of Elks. Royal Arcanum. Clubs: Young Men's, Regular Republican.
Married Martha Armitage, 1899 (deceased).; married second, Mabelle Sylvester Weston, May 14, 1932. Children: Lloyd, Caleb.