The dynamic performance of a photovoltaic direct-expansion solar heat-pump water heater (PV-DX-SHPWH) with 110 L capacity and driven by a photovoltaic array and the electric grid is analyzed by means of a validated numerical dynamic model considering typical meteorological conditions in Medellin, Colombia. Refrigerant R1234yf is selected as the working fluid due to its low global warming potential and its zero ozone depletion potential. A photovoltaic panel system is included as the main power source for a DC variable speed compressor in order to harness a renewable source of energy, while the grid is a backup source of energy. After validating the numerical approach by comparison to experimental data from the literature, the behavior of the PV-DX-SHPWH is simulated for values of installed photovoltaic peak power between 200 and 1000 W during a complete Typical Meteorological Year (TMY) to obtain indicators of the average thermal performance. From these simulation results, thermal performance for three representative days is analyzed in detail in terms of evolution of water temperature and coefficient of performance (COP). Also, an economic analysis is performed for the yearlong simulation results in terms of the levelized cost of heat (LCOH), and the results for the PV-DX-SHPWH are compared with other traditional water heating systems. According to the thermo-economic analysis, the COP of the system is higher at low installed photovoltaic powers, and a photovoltaic power range is found whereby high performance of the system is achieved at a low LCOH, and whereby the proposed system is more competitive than other alternatives for water heating.