A method for manufacturing oriented arrays of ceramic or metal oxide nanostructures, such as titania (TiO.sub.2) nanofibers. The nanofibers are formed on the surface of a body that is first sintered at a temperature in the range of about 1,100 to about 1,400 degrees Celsius. Subsequently, the surface is exposed to an H.sub.2-bearing gas, such as H.sub.2 and N.sub.2 in a ratio of about 5:95 at about 700 degrees Celsius for about 8 hours. During heat treatment in the gas phase reaction, sintered titania grains transform into arrays of nanofibers oriented in the same crystallographic direction.