Short final is not defined by ICAO, although interestingly the term is used in an example in the ICAO Manual of Radiotelephony. Some States may have defined the term - the UK has not.
It can probably be best summed up in practice as indicating a degree of urgency when used by the pilot (as in 'Well, can I land or not?') or perhaps as a reminder when used by a controller so tht he/she does not have to continually watch an aircraft as it goes around the circuit. I would expect the range that qualifies as short final to vary with the aircraft type/size/speed. For a Boeing or Airbus I would go with TopBunk and say inside 1 mile would commonly be called short final but for a C150 inside half a mile and maybe even coming over the LLZ would not be an uncommon view.