We report theoretical investigations on the transient dynamics of a ground state Hanle effect in the Voigt geometry, where a time-varying scanning magnetic field B(t) is applied perpendicular to the light propagation direction. Transient Hanle signals are calculated for different light polarizations using a theoretical model based on the density matrix approach. First, we studied the ellipticity dependence of transient Hanle signals in two configurations in which the major axis of light polarization ellipse ( ε_a) is aligned either perpendicular or parallel to the field B. For ε_a⊥B, elliptical polarization of the light produces oscillations of frequencies 2ΩL(t) and ΩL(t) simultaneously, where ΩL(t) is the Larmor frequency of corresponding field B(t). On the other hand, in case of ε_a|| B, only ΩL(t) oscillation is observed using an elliptically polarized light. Second, we vary the tilt angle between the polarization vector of a linearly polarized light and the orientation of the field B and studied its effect on the transient response of Hanle signals. Both the amplitude and the decay rate of oscillations show a strong dependence on the light ellipticity and tilt angle of polarization vector. In addition, the influence of magnetic field sweep rate on the transient signals is also demonstrated for given values of light ellipticity and polarization angle.