Metal halide perovskites of the general formula ABX-where A is a monovalent cation such as caesium, methylammonium or formamidinium; B is divalent lead, tin or germanium; and X is a halide anion-have shown great potential as light harvesters for thin-film photovoltaics. Among a large number of compositions investigated, the cubic α-phase of formamidinium lead triiodide (FAPbI) has emerged as the most promising semiconductor for highly efficient and stable perovskite solar cells, and maximizing the performance of this material in such devices is of vital importance for the perovskite research community. Here we introduce an anion engineering concept that uses the pseudo-halide anion formate (HCOO) to suppress anion-vacancy defects that are present at grain boundaries and at the surface of the perovskite films and to augment the crystallinity of the films. The resulting solar cell devices attain a power conversion efficiency of 25.6 per cent (certified 25.2 per cent), have long-term operational stability (450 hours) and show intense electroluminescence with external quantum efficiencies of more than 10 per cent. Our findings provide a direct route to eliminate the most abundant and deleterious lattice defects present in metal halide perovskites, providing a facile access to solution-processable films with improved optoelectronic performance.