We explore a new platform for realizing excitonic insulators, namely van der Waals (vdW) bilayers comprising two-dimensional Janus materials. In previous studies, type II heterobilayers have been brought to the excitonic insulating regime by tuning the band alignment using external gates. In contrast, the Janus bilayers presented here represent intrinsic excitonic insulators. We first conduct ab initio calculations to obtain the quasiparticle band structures, screened Coulomb interaction, and interlayer exciton binding energies of the bilayers. These ab initio-derived quantities are then used to construct a BCS-like Hamiltonian of the exciton condensate. By solving the mean-field gap equation, we identify 16 vdW Janus bilayers with insulating ground states and superfluid properties. Our calculations expose a new class of advanced materials that are likely to exhibit novel excitonic phases at low temperatures and highlight the subtle competition between interlayer hybridization, spin-orbit coupling, and dielectric screening that governs their properties.