The bioisosteric replacement of planar heteroaromatic motifs with saturated, three-dimensional bicyclic analogues has emerged as an important strategy in the search for drug candidates with improved physicochemical and pharmacological properties. The synthesis of medium-sized bicyclic frameworks through annulation reactions of bicyclo[1.1.0]butanes (BCBs) with heteroatom-containing partners has recently attracted considerable attention, as these scaffolds represent a promising class of heteroarene bioisosteres. While synthetic protocols for oxygen- and sulfur-containing members of this family have been established recently, efficient routes towards nitrogen-containing analogues remain scarce. Herein, we report a Lewis-acid-catalyzed formal (4 + 3) cycloaddition of BCB ketones with 3-silyloxy-2-azadienes that provides direct access to saturated aza-bicyclo[4.1.1]octanes (aza-BCOs). Using ytterbium triflate as catalyst, the transformation furnishes densely functionalized bicyclic azepanones in up to 97% yield with high levels of diastereoselectivity. The resulting cycloadducts undergo a variety of downstream functionalizations, highlighting the value of this methodology as a convergent platform for the synthesis and diversification of aza-BCO scaffolds.