We present a novel mixed quantum-classical approach to the coupled electron-nuclear dynamics based on the exact factorisation of the electron-nuclear wave function, recently proposed in Abedi, A., Maitra, N. T. and Gross, E. K. U., Phys. Rev. Lett., 105 (2010) 123002. In this framework, the correct classical limit of the nuclear dynamics is worked out by taking the classical limit of the exact time-dependent Schrödinger equation satisfied by the nuclear wave function. The effect of the time-dependent scalar and vector potentials, representing the exact electronic back-reaction on the nuclear subsystem, is consistently derived within the classical approximation. We examine with an example the performance of the proposed mixed quantum-classical scheme in comparison with exact calculations.