Metastable γ'' (D022-Ni3Nb) particles with three variations in orientation are strengthening precipitates for commercial Inconel 625 Ni-based superalloy. Understanding whether their morphological evolution or their fractions inside a RVE matrix is critical for evaluating hardening effects and guiding designing additive manufacturing process to improve its yield strength. A computational coupled phase-field model was developed to predict solid-state phase transformation kinetics within mechanical parts during metal additive manufacturing processes, to take into account the heat accumulated during printing. During precipitation the time evolution of the concentration fields is governed by the generalized diffusion equation, i.e. the Cahn–Hilliard equations while the time-evolution of the structural order parameter (herein phases) is governed by the time-dependent Allen-Cahn equation. The precipitation model is quantitative, using as model inputs ab initio calculations of elastic constants, experimental data on lattice parameters, precipitate-matrix orientation relationship, and interfacial energy of each individual precipitate phase and inter-diffusivities, and a Ni–Nb–Al pseudo-ternary thermodynamic database specifically developed for IN625. Simulation results show how alloy composition, lattice misfit, external stress, temperature and time affect precipitate microstructure and variant selection during non-isothermal heat history fluctuation, without any a priori assumptions about key microstructural features including size, shape, volume fraction and spatial distribution of different types of precipitates and different variants of the same precipitate phase.