We present an analytical model to account for the deformation-induced inertial dynamics of a magnetic vortex. The model is based on a deformation of the vortex core profile based on the Döring kinetic field, whereby the deformation amplitudes are promoted to dynamical variables in a collective-coordinate approach that provides a natural extension to the Thiele model. This extended model describes complex transients due to inertial effects and the variation of the effective mass with velocity. The model also provides a quantitative description of the inertial dynamics leading up to vortex core reversal, which is analogous to the Walker transition in domain wall dynamics. Our work paves the way for a standard prescription for describing the inertial effects of topological magnetic solitons.