A structure for the covering of surfaces, comprising: - a fixing bracket having a connecting portion, preferably planar, stably anchored to a bearing structure, and a hooking portion integral with the connecting portion and defining a concave seat; - a first panel and a second panel, each having a main portion and, on opposite sides of said main portion, a first hooking portion at least partially shaped, projecting from said main portion, and a second hooking portion at least partially shaped, projecting from said main portion, wherein said first panel also has an end relief arranged adjacent to said first hooking portion; preferably the second hooking portion of the second panel being complementary shaped with respect to the first hooking portion of the first panel; in a configuration of use, the second hooking portion of the second panel being applied on the first hooking portion of the first panel according to a unique and predetermined positioning, in particular by means of a shape coupling, in such a way that the second panel clads the first panel at said hooking portions (6, 7) coupled together; wherein the hooking portion of the fixing bracket is configured to interpose, in said configuration of use, between the first panel and the second panel and to house said end relief inside said concave seat; the structure further comprising an anchoring bracket which can be fixed to the bearing structure and shaped so as to define a mounting portion on which said connecting portion of the fixing bracket is applicable in use; wherein the structure comprises first connecting means for the stable fixing of the anchoring bracket to the bearing structure and second connecting means for the stable fixing of the fixing bracket to the mounting portion of the anchoring bracket, characterised in that said anchoring bracket has a receiving surface configured to receive and support an end portion of the first panel interposed between the first hooking portion and said end relief. - a fixing bracket having a connecting portion, preferably planar, stably anchored to a bearing structure, and a hooking portion integral with the connecting portion and defining a concave seat; - a first panel and a second panel, each having a main portion and, on opposite sides of said main portion, a first hooking portion at least partially shaped, projecting from said main portion, and a second hooking portion at least partially shaped, projecting from said main portion, wherein said first panel also has an end relief arranged adjacent to said first hooking portion; preferably the second hooking portion of the second panel being complementary shaped with respect to the first hooking portion of the first panel; in a configuration of use, the second hooking portion of the second panel being applied on the first hooking portion of the first panel according to a unique and predetermined positioning, in particular by means of a shape coupling, in such a way that the second panel clads the first panel at said hooking portions (6, 7) coupled together; the structure further comprising an anchoring bracket which can be fixed to the bearing structure and shaped so as to define a mounting portion on which said connecting portion of the fixing bracket is applicable in use; wherein the structure comprises first connecting means for the stable fixing of the anchoring bracket to the bearing structure and second connecting means for the stable fixing of the fixing bracket to the mounting portion of the anchoring bracket, characterised in that said anchoring bracket has a receiving surface configured to receive and support an end portion of the first panel interposed between the first hooking portion and said end relief.