High-resolution climate projections provide crucial insights into assessing climate risk and developing climate resilience strategies. The Seasonal Trends and Analysis of Residuals empirical statistical downscaling model (STAR-ESDM) is a computationally-efficient and flexible approach to generating high-resolution climate projections that can be applied globally using a broad range of predictands and predictors that can be sourced from weather stations, gridded datasets, satellites, reanalysis, and global or regional climate models. It uses signal processing combined with Fourier filtering and kernal density estimation techniques to decompose and smooth any quasi-Gaussian time series, gridded or point-based, into multi-decadal long-term means and/or trends; static and dynamic annual cycles; and probability distributions of high-frequency variability. Long-term predictor trends are bias-corrected and predictor components are used to map remaining predictand components to future conditions. Components are then recombined for each station or grid cell to produce a continuous, high-resolution bias-corrected and downscaled time series at the spatial and temporal scale of the original time series. Comparing STAR-ESDM output with high-resolution daily temperature and precipitation projections generated by a fully dynamical global model demonstrates that the method is extremely robust, capable of accurately reproducing projected changes for all but the most extreme temperature and precipitation values. For most continental areas, biases in 1-in-1000 hottest and coldest temperatures are less than 0.5°C and biases in the 1-in-1000 wet day precipitation amounts are less than 5 mm/day. As climate impacts intensify, STAR-ESDM represents a significant advance in generating consistent high-resolution projections to comprehensively assess risk and optimize resilience.