Geography and landscape are important determinants of genetic variation in natural populations, and several ancestry estimation methods have been proposed to investigate population structure using genetic and geographic data simultaneously. Those approaches are often based on computer-intensive stochastic simulations and do not scale with the dimensions of the data sets generated by high-throughput sequencing technologies. There is a growing demand for faster algorithms able to analyse genomewide patterns of population genetic variation in their geographic context. In this study, we present TESS3, a major update of the spatial ancestry estimation program TESS. By combining matrix factorization and spatial statistical methods, TESS3 provides estimates of ancestry coefficients with accuracy comparable to TESS and with run-times much faster than the Bayesian version. In addition, the TESS3 program can be used to perform genome scans for selection, and separate adaptive from nonadaptive genetic variation using ancestral allele frequency differentiation tests. The main features of TESS3 are illustrated using simulated data and analysing genomic data from European lines of the plant species Arabidopsis thaliana.