Process-structure-property (PSP) relationships are critical to the optimization of manufacturing processes, but establishing these relationships typically involves time- and cost- consuming experiments, especially for additive manufacturing (AM) due to the large number of process parameters involved. In this study, we develop a novel and interpretable machine learning approach for predicting, optimizing, and expanding the process window of laser powder bed fusion (LPBF) while simultaneously establishing PSP relationships, using AlSi10Mg as an example. Our iterative, error-targeted method substantially decreases the amount of experimentation required. Gaussian process regression (GPR) was employed as the predictive model, incorporating multiple input variables (e.g., process parameters, relative density, melt pool morphology, cellular structure, and grain structure), for predicting three mechanical properties (i.e., yield strength, ultimate tensile strength, and % elongation). A comparison of model predictions and experimental data outside the training scope reveals that the prediction accuracy can be improved with higher dimensional inputs and further enhanced by a multi-output model that accounts for correlations between the different mechanical properties. Additionally, the GPR kernel’s hyperparameter for each input enables feature selection and model interpretability. The proposed approach can assist with finding the most critical variables affecting mechanical performance, establishing the PSP relationships of AM fabricated alloys, and providing guidance for tailoring the final properties. The methodology presented in this study can be applied to various AM techniques and materials to broaden the process window to achieve previously unattainable mechanical properties, as well as to gain a deeper understanding of the PSP relationships.