In this letter, we outline a methodology to calculate microscopically mass and charge distributions of spontaneous fission yields. We combine the multi-dimensional minimization of collective action for fission with stochastic Langevin dynamics to track the relevant fission paths from the ground-state configuration up to scission. The nuclear potential energy and collective inertia governing the tunneling motion are obtained with nuclear density functional theory in the collective space of shape deformations and pairing. We obtain a quantitative agreement with experimental data and find that both the charge and mass distributions in the spontaneous fission of 240Pu are sensitive both to the dissipation in collective motion and to adiabatic characteristics.