A wheat variety designated 25R40, the plants and seeds of wheat variety 25R40, methods for producing a wheat plant produced by crossing the variety 25R40 with another wheat plant, and hybrid wheat seeds and plants produced by crossing the variety 25R40 with another wheat line or plant, and the creation of variants by mutagenesis or transformation of variety 25R40. This invention also relates to methods for producing other wheat varieties or breeding lines derived from wheat variety 25R40 and to wheat varieties or breeding lines produced by those methods.