This technical design report (TDR) of the High Energy Density Physics scientific instrument (HED instrument) at the European XFEL outlines the scientific and technological requirements for the various subsystems and describes the technical realization of the instrument chosen to match these requirements.The scientific requirements have been extracted from a range of proposed scientific applications at HED. Most of these applications had been discussed in the past years as the core of the scientific activity at HED, but, with the recent start of operation of the Matter under Extreme Conditions instrument at the Linac Coherent Light Source (LCLS) at SLAC National Accelerator Laboratory in Menlo Park, California, several new ideas and applications have been included. High energy density (HED) matter is generally defined as having an energy density above 1011 J•$m^{-3}$, which is equivalent to 100 GPa (1 Mbar) pressure and 500 T magnetic pressure.