This study provides a thorough investigation of microstructural heterogeneity and its relationship to the mechanical properties of Inconel 625 (IN625) alloy in as-built Laser Powder Bed Fusion (LPBF) parts. Specifically, detailed high-resolution electron microscopy coupled with thermodynamic simulation, finite element analysis, and nano-hardness testing were carried out. Through the combination of these methods, a new method is proposed to develop a process-structure–property map to illustrate the complex relationship between spatial thermal conditions, microstructure, and mechanical properties in various areas of an LPBF IN625 sample. Different precipitates, including γ′′, Laves, NbC, and Al2O3 oxide were observed along the build direction from the bottom to the top layers of the LPBF part as a function of build height. The hardness value was shown to be minimum in the middle layers while attaining maximum values in the bottom (near the substrate) and top (near the surface) layers of the build’s height. The mechanism for the formation of precipitates during multi-layer additive manufacturing and the dependency of the mechanical properties on the type and distribution of these precipitates are discussed.