Exact solution in analytical form to the dopant diffusion equation for an arbitrary initial implanted profile is obtained with a judicious choice of variables. The diffusivity can be an arbitrary function of the dopant concentration and the temperature of a sample, provided only that their gradients at the front surface of an ion‐implanted semi‐infinite semiconductor wafer are zero. As an example, we derive a closed‐form expression for the annealed concentration profile for the special case in which the diffusivity is a product of a certain power of the concentration and an arbitrary function of the temperature, the initial dopant concentration profile is a truncated Gaussian, and the temperature dependent part of the diffusivity is initially a Gaussian. The present calculation is a generalization of the data fitting analysis of ion‐implanted dopant profile evolution during annealing by R. Ghez, A. S. Oehrlein, T. O. Sedgwick, F. F. Morehead, and Y. H. Lee [Appl. Phys. Lett. 45, 881 (1984)].