Bicyclo[1.1.0]butane-containing compounds feature a unique chemical reactivity, trigger "strain-release" reaction cascades, and provide novel scaffolds with considerable utility in the drug discovery field. We report the synthesis of new bicyclo[1.1.0]butane-linked heterocycles by a nucleophilic addition of bicyclo[1.1.0]butyl anions to 8-isocyanatoquinoline, or, alternatively, iminium cations derived from quinolines and pyridines. The resulting bicyclo[1.1.0]butanes are converted with high regioselectivity to unprecedented bridged heterocycles in a rhodium(I)-catalyzed annulative rearrangement. The addition/rearrangement process tolerates a surprisingly large range of functional groups. Subsequent chemo- and stereoselective synthetic transformations of urea, alkene, cyclopropane, and aniline moieties of the 1-methylene-5-azacyclopropa[cd]indene scaffolds provide several additional new heterocyclic building blocks. X-ray structure-validated quantum mechanical DFT calculations of the reaction pathway indicate the intermediacy of rhodium carbenoid and metallocyclobutane species.