Inconel 625, also referred to as 5599 Nickel Superalloy, is a nickel-based superalloy widely used in applications such as jet engine exhaust systems, marine components exposed to seawater, and fasteners or cable connectors. In this study, the effects of the annealing process on the mechanical properties and vibrational behavior of the alloy were investigated both at room temperature and at 950 °C. Comprehensive analyses were performed on Inconel 625, including microhardness measurements, true stress–true strain characterization, vibrational testing, and SEM/EDS examinations. The results revealed a notable 30% increase in hardness and a 50% improvement in toughness after annealing. Furthermore, experimental vibration measurements showed that the annealing process significantly reduced the damping ratio (from 0.0249 to 0.012) by eliminating dislocations and internal stresses that typically act as energy-dissipating mechanisms.