The nuclear and magnetic structures of Fe1+yTe1−xSex compounds was analyzed between 2 and 300 K by means of Rietveld refinement of neutron powder diffraction data. Samples with x<0.075 undergo a tetragonal to monoclinic phase transition at low temperature, whose critical temperature decreases with increasing Se content; this structural transition is strictly coupled to a long-range antiferromagnetic ordering at the Fe site. Both the transition to a monoclinic phase and the long-range antiferromagnetism are suppressed for 0.10<x<0.20. The onset of the structural and of the magnetic transition remains coincident with the increase in Se substitution. The low-temperature monoclinic crystal structure has been revised. Superconductivity arises for x<0.05, therefore a significant region where superconductivity and long-range antiferromagnetism coexist is present in the pseudobinary FeTe-FeSe phase diagram.