We present a new method for simulating heterogeneous (surface and multiphase) cloud chemistry in atmospheric models that do not spatially resolve clouds. The method accounts for cloud entrainment within the chemical rate expression, making it more accurate and stable than other approaches. Using this “entrainment‐limited uptake,” we evaluate the role of clouds in the tropospheric NOx cycle. Past literature suggests that on large scales, losses of N2O5 and NO3 in clouds are much less important than losses on aerosols. We find, however, that cloud reactions provide 25% of tropospheric NOx loss in high latitudes and 5% of global loss. Homogeneous, gas phase hydrolysis of N2O5 is likely 2% or less of global NOx loss. Both clouds and aerosols have similar impacts on global tropospheric O3 and OH levels, around 2% each. Accounting for cloud uptake reduces the sensitivity of atmospheric chemistry to aerosol surface area and uptake coefficient since clouds and aerosols compete for the same NO3 and N2O5. Plain Language Summary Cloud water droplets and ice crystals enable some aqueous and surface chemical reactions that otherwise would not occur in the gaseous atmosphere. While clouds are widespread and familiar, methods for simulating their multiphase chemical effects in global atmospheric models have been inadequate. We present an efficient mathematical method to represent the combined effects of cloud chemistry and entrainment in large‐scale atmospheric chemistry models that do not resolve individual clouds. By applying the approach to nitrogen oxides, we show that clouds have a previously unrecognized impact on tropospheric ozone, an air pollutant and greenhouse gas, and hydroxyl, a key atmospheric oxidant.