A hypersurface in the Euclidean space \(\mathbb {R}^{n+1}\) is called a translation hypersurface if it can be expressed as \(x_{n+1}=\sum \nolimits _{i=1}^n f_i(x_i)\) , where all \(f_i\) are smooth functions of one variable. In this paper, we give a full classification of the translation hypersurfaces that are solitons of the mean curvature flow. We prove that a translation hypersurface \(\Sigma \) , which is a soliton of the mean curvature must be, after renaming the coordinates, a Euclidean product \(\mathbb {R}^{n-1}\times \Gamma \) , where the planar curve \(\Gamma \subset \mathbb {R}^2\) is a 2-dimensional soliton of the curvature.
