ICAO Annex 6 holds the answer.
For commercial aviation (annex 6 part I):
6.3.1.1 Types
6.3.1.1.1 Types I and IA FDR shall record the parameters required to determine accurately the aeroplane flight path, speed, attitude, engine power, configuration and operation.
6.3.1.1.2 Types II and IIA FDRs shall record the parameters required to determine accurately the aeroplane flight path, speed, attitude, engine power and configuration of lift and drag devices.
6.3.1.2 Operation
6.3.1.2.1 All turbine-engined aeroplanes of a maximum certificated take-off mass of 5 700 kg or less for which a type certificate is first issued on or after 1 January 2016 shall be equipped with:
a) a Type II FDR; or
b) a Class C AIR capable of recording flight path and speed parameters displayed to the pilot(s); or
c) an ADRS capable of recording the essential parameters defined in Table A8-3 of Appendix 8.
6.3.1.2.3 All aeroplanes of a maximum certificated take-off mass of over 27 000 kg for which the individual certificate of airworthiness is first issued on or after 1 January 1989 shall be equipped with a Type I FDR.
6.3.1.2.4 All aeroplanes of a maximum certificated take-off mass of over 5 700 kg, up to and including 27 000 kg, for which the individual certificate of airworthiness is first issued on or after 1 January 1989, shall be equipped with a Type II FDR.
For general aviation (annex 6 part II):
3.6.3.3 Flight data recorders - aeroplanes for which the individual certificate of airworthiness is first issued on or after January 1989
3.6.3.3.1 All aeroplanes of a maximum certificated take-off mass of over 27 000 kg shall be equipped with a Type I flight data recorder.
3.6.3.4 Flight data recorders - aeroplanes for which the individual certificate of airworthiness is first issued after i January 2005
All aeroplanes of a maximum certificated take-off mass of over 5 700 kg shall be equipped with a Type IA flight data recorder.
As rules and regulations tend to change from time to time, you should always check the latest edition of ICAO Annex 6 for current requirements.