This paper tackles the problem of users assignment to evolved NodeBs in long‐term evolution mobile networks. We propose a model that aims at assigning users by minimizing a function called download time of the complete system, defined as the minimum time required for all the users in the system to complete their downloads. This strategy helps the network use its resources in a more balanced way, by assigning users from cells (which otherwise would be overloaded when using a simple signal‐to‐interference‐plus‐noise ratio‐based approach) to others with less load. The user‐cell association problem is, in general, a combinatorial NP hard problem. Although other approaches indirectly tackle this complexity by transforming the problem into another whose optimal solution is less difficult (but still with very high computational cost), we tackle directly our download time of the complete system minimization problem by finding an approximate solution provided by a specific implementation of an evolutionary algorithm, which is based on a long‐term evolution domain‐specific initial population along with fully tailored operators adapted to this assignment problem. A variety of experiments in different realistic scenarios point out that the proposed method outperforms the conventional signal‐to‐interference‐plus‐noise ratio‐based and load balancing approaches, specially in urban and dense urban environments (where the assignment is more critical in terms of capacity). We have also tested our approach in simple scenarios that mimic heterogeneous networks and ultra‐dense networks in which the number of users is similar to that of nodes, proving its beneficial properties. Our method is aimed at the design/dimensioning stage and not to the operation stage, and in this sense, it is an off‐line algorithm that could be useful to make better decisions on cost‐effective network dimensioning and upgrading.