An analytical solution of Fick's diffusion equation for the formation of a 2D solid-phase involving a growing front (Stefan problem) position changing at a constant linear velocity is proposed. This solution comprises a first diffusion term that includes an exponential correction factor, and a second constant advection term that depends on the front velocity, and it predicts a kinetic transition from a diffusion to an advection-dominated mass transfer control in going from t --> 0 to t --> infinity. The validity of the analytical solution is tested using potentiostatic cathodic current transient data for silver electrodeposition in a quasi-2D rectangular cell with an initially plane plate cathode. Theoretical and experimental data fulfill a dimensionless correlation after experimental data are properly corrected for the effective cathode area.