Cometary nuclei imaged from flyby and rendezvous spacecraft show common evidence of layered structures and bilobed shapes. But how and when these features formed is much debated, with distinct implications for solar system formation, dynamics, and geology. We show that these features could be a direct result of accretionary collisions, based on three-dimensional impact simulations using realistic constitutive properties. We identify two regimes of interest: layer-forming splats and mergers resulting in bilobed shapes. For bodies with low tensile strength, our results can explain key morphologies of cometary nuclei, as well as their low bulk densities. This advances the hypothesis that nuclei formed by collisional coagulation-either out of cometesimals accreting in the early solar system or, alternatively, out of comparable-sized debris clumps paired in the aftermath of major collisions.