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The use of post-processing heat treatments is often considered a necessary approach to relax high-magnitude residual stresses (RS) formed during the layerwise additive manufacturing laser powder bed fusion (LPBF). In this work, three heat treatment strategies using temperatures of 450 °C, 800 °C, and 900 °C are applied to austenitic stainless steel 316L samples manufactured by LPBF. These temperatures encompass the suggested lower and upper bounds of heat treatment temperatures of conventionally processed 316L. The relaxation of the RS is characterized by neutron diffraction (ND), and the associated changes of the microstructure are analyzed using electron backscattered diffraction (EBSD) and scanning electron microscopy (SEM). The lower bound heat treatment variant of 450 °C for 4 hours exhibited high tensile and compressive RS. When applying subsequent heat treatments, we show that stress gradients are still observed after applying 800 °C for 1 hour but almost completely vanish when applying 900 °C for 1 hour. The observed near complete relaxation of the RS appears to be closely related to the evolution of the characteristic subgrain solidification cellular microstructure.