The gaseous air pollutants nitrogen dioxide (NO2), ozone (O3), and sulfur dioxide (SO2), in addition to particulate matter (PM2.5), are known to be associated with many adverse health effects. However, exposure estimates may not be available in rural or mountainous areas without monitoring stations. In this study, we retrieved satellite remote sensing data for NO2, O3, and SO2 from the Ozone Monitoring Instrument (OMI) L3 products. Together with ground measurements (air monitoring stations and meteorological and land use data), we estimated the monthly NO2, O3, and SO2 concentrations with a spatial resolution of 3×3 km across Taiwan from 2005 to 2019. A three-stage estimation procedure was utilized: in Stage 1, an ensemble generalized additive model (GAM) and machine learning method were used to determine the spatiotemporal variations; in Stage 2, the remote sensing data were downscaled; and in Stage 3, the downscaled concentrations were reused in the Stage 1 procedure for fine-tuning estimations. We obtained overall leave-one-out cross-validation (LOOCV) R2 values ranging from 0.927-0.950, 0.704-0.721, and 0.601-0.716, and root-mean-square-errors (RMSEs) ranging from 1.59-2.28, 3.81-4.18, and 0.67-1.32 ppb for NO2, O3, and SO2, respectively, via the random forest procedure. The annual NO2 and SO2 concentrations greatly improved from 2005-2019, especially in the western residential area of Taiwan. However, despite these improvements in air quality, the annual O3 concentrations tended to increase from 2015–2019. This might be due to the complex mixtures of precursors (e.g., NO2), atmospheric circulation, barriers of the Central Mountain Ridge, and increasing ground temperatures over the past decade. The proposed multistage estimation procedure performed well over the whole island with complex terrain and topography. The study outcomes may provide epidemiological information for long-term ambient exposure estimates and guidance for future administrative policies.