The solution processing of polycrystalline perovskite films introduces trap states that can adversely affect their optoelectronic properties. Motivated by the use of small-molecule surfactants to improve the optoelectronic performance of perovskites, we demonstrate the use of polymers with coordinating groups to improve the performance of solution-processed semiconductor films. The use of these polymer modifiers results in a marked change in the electronic properties of the films, as measured by both carrier dynamics and overall device performance. The devices grown with the polymer poly(4-vinylpyridine) (PVP) show significantly enhanced power conversion efficiency from 16.9 ± 0.7% to 18.8 ± 0.8% (champion efficiency, 20.2%) from a reverse scan and stabilized champion efficiency from 17.5 to 19.1% [under a bias of 0.94 V and AM (air mass) 1.5-G, 1-sun illumination over 30 min] compared to controls without any passivation. Treating the perovskite film with PVP enables a V_OC of up to 1.16 V, which is among the best reported for a CH₃NH₃PbI₃ perovskite solar cell and one of the lowest voltage deficits reported for any perovskite to date. In addition, perovskite solar cells treated with PVP show a long shelf lifetime of up to 90 days (retaining 85% of the initial efficiency) and increased by a factor of more than 20 compared to those without any polymer (degrading to 85% after ~4 days). Our work opens up a new class of chemical additives for improving perovskite performance and should pave the way toward improving perovskite solar cells for high efficiency and stability.