We propose a new method to linearize cosmological mass density fields using higher order Lagrangian perturbation theory (LPT). We demonstrate that a given density field can be expressed as the sum of a linear and a non-linear component which are tightly coupled to each other by the tidal field tensor within the LPT framework. The linear component corresponds to the initial density field in Eulerian coordinates, and its mean relation with the total field can be approximated by a logarithm (giving theoretical support to recent attempts to find such a component). We also propose to use a combination of the linearization method and the continuity equation to find the mapping between Eulerian and Lagrangian coordinates. In addition, we note that this method opens the possibility of using directly higher order LPT on non-linear fields. We test our linearization scheme by applying it to the z ∼ 0.5 density field from an N-body simulation. We find that the linearized version of the full density field can be successfully recovered on ≳5 h−1 Mpc, reducing the skewness and kurtosis of the distribution by about one and two orders of magnitude, respectively. This component can also be successfully traced back in time, converging towards the initial unevolved density field at z ∼ 100. We anticipate a number of applications of our results, from predicting velocity fields to estimates of the initial conditions of the Universe, passing by improved constraints on cosmological parameters derived from galaxy clustering via reconstruction methods.