We herein report a copper-catalyzed 1,3-aminocyclization of cyclopropanes as a direct and versatile entry into important heterocycles. This reaction was initiated by a copper-catalyzed, NFSI-promoted ring opening of cyclopropanes, followed by nucleophilic cyclization. A variety of nucleophiles successfully participate in this transformation, including alcohols, carboxylic acids, sulfonamides, and amides, for the construction of diverse cyclic ethers, pyrrolidines, lactones, and iminolactones.