All-perovskite–based polycrystalline thin-film tandem solar cells have the potential to deliver efficiencies of >30%. However, the performance of all-perovskite–based tandem devices has been limited by the lack of high-efficiency, low–band gap tin-lead (Sn-Pb) mixed-perovskite solar cells (PSCs). We found that the addition of guanidinium thiocyanate (GuaSCN) resulted in marked improvements in the structural and optoelectronic properties of Sn-Pb mixed, low–band gap (~1.25 electron volt) perovskite films. The films have defect densities that are lower by a factor of 10, leading to carrier lifetimes of greater than 1 microsecond and diffusion lengths of 2.5 micrometers. These improved properties enable our demonstration of >20% efficient low–band gap PSCs. When combined with wider–band gap PSCs, we achieve 25% efficient four-terminal and 23.1% efficient two-terminal all-perovskite–based polycrystalline thin-film tandem solar cells.