The tunability of the exciton g factor in InGaAs quantum dots using compressive biaxial stress applied by piezoelectric actuators is investigated. We find a clear relation between the exciton g factor and the applied stress. A linear decrease of the g factor with compressive biaxial strain is observed consistently in all investigated dots. A connection is established between the response of the exciton g factor to the voltage applied to the piezoelectric actuator and the response of the quantum dot emission energy. We employ a numerical model based on eight-band k⋅p theory to calculate the exciton g factor of a typical dot as a function of strain and a good agreement with our experiments is found. Our calculations reveal that the change in exciton g factor is dominated by the contribution of the valence band and originates from increased heavy hole light hole splitting when applying external stress.