This work presents an analytical solution for the transient three-dimensional advection-diffusion equation to simulate the dispersion of pollutants in the atmosphere. The solution of the advection-diffusion equation is obtained analytically using a combination of the methods of separation of variables and GILTT. The main advantage is that the presented solution avoids a numerical inversion carried out in previous works of the literature, being by this way a totally analytical solution, less than a summation truncation. Initial numerical simulations and statistical comparisons using data from the Copenhagen experiment are presented and prove the good performance of the model.