We theoretically study the impact of changes in surroundings on the electron ground-state effective g factor in defect-free GaAs/AlGaAs nanodisks. To perform the study, we formulate and deploy a computational efficient full three-dimensional model to describe the effective g-factor tensor in semiconductor nano-objects of complex geometry and material content. This model is based on an effective 2 × 2 conduction-band Hamiltonian which includes the Rashba and Dresselhaus spin-orbit couplings. The description is suited to clarify the important question of the controllability of the electron effective g factor in semiconductor nano-objects. The results of this theoretical study suggest that in the defect-free GaAs/AlGaAs nanodisks, the effective g factor can be tuned within a wide range by proper design of the nanodisk environment. The zz components of the electron effective g-factor tensor obtained in our simulation are in good agreement with some recent experimental observations.