The invention relates to a method for constructing buildings having a reticular structure and to a building constructed using said method. The method comprises the steps of: erecting a set of columns (1, 2, 3, 4) that form the vertical supporting structure, on foundations or piles; arranging, in a lower zone of the structure (100), a heap (5) with fully constructed floor modules (6) inside the space defined by the columns (1, 2, 3, 4) and in the same vertical order as the definitive order planned for each of the floor modules of the structure (100) forming the building; raising the floor modules (6) by means of elevators, to place same in their definitive positions at corresponding heights; and joining the floor modules (6) to the columns (1, 2, 3, 4) by means of screwing, welding, riveting or an equivalent system.