The possibility of lead (Pb) contamination and the volatility of the organic cations in the prevailing Pb-based organic-inorganic perovskite (HP) light absorbers are the two key issues of concern in the emerging perovskite solar cells (PSCs). The majority of the Pb-free HP candidates that are being explored for PSCs either suffer from instability issues and have unfavorable defect properties or have unsuitable bandgaps for PSC applications. We report the prediction of a promising new family of all-inorganic HPs based on the nontoxic, earth-abundant, ultrastable Ti(IV) for use in PSCs. We show that the Ti-based HPs possess a combination of several desirable attributes, including suitable bandgaps, excellent optical absorption, benign defect properties, and high stability. In particular, we show experimentally that representative members of the Ti-based HP family, Cs₂TiI_xBr_6–x, have bandgaps that can be tuned between the ideal values of 1.38 and 1.78 eV for single-junction and tandem photovoltaic applications, respectively.