This work deals with the effects of two individual isothermal aging experiments (450 °C/5000 h and 700 °C/2500 h) and the subsequent room-temperature electrolytic hydrogen charging of TP316H stainless steel on its Charpy V-notch (CVN) impact toughness and fracture behavior at room temperature. Microstructural analyses revealed that aging at 700 °C resulted in the abundant precipitation of intermediary phases, namely, the Cr23C6-based carbide phase and Fe2Mo-based Laves phase, whereas aging at 450 °C resulted in much less pronounced precipitation of mostly intergranular Cr23C6-based carbides. The matrix phase of 700 °C-aged material was completely formed of austenitic solid solution with a face-centered cubic (FCC) crystal structure, whereas an additional formation of ferritic phase with a base-centered cubic (BCC) structure was detected in 450 °C-aged material. The performed microstructure observations correlated well with the obtained values of CVN impact toughness, i.e., a sharp drop in the impact toughness was observed in the material aged at 700 °C, whereas negligible property changes were observed in the material aged at 450 °C. The initial, solution-annealed (precipitation-free) TP316H material exhibited a notable hydrogen toughening effect after hydrogen charging, which has been attributed to the hydrogen-enhanced twinning-induced plasticity (TWIP) deformation mechanism of the austenitic solid solution. In contrast, both aging expositions resulted in significantly lowered hydrogen embrittlement resistance, which was likely caused by hydrogen trapping effects at the precipitate/matrix interfaces in thermally aged materials, leading to a reduced TWIP effect in the austenitic phase.