Genomic evidence supports an important role for selection in shaping patterns of introgression along the genome, but frameworks for understanding the dynamics underlying these patterns within hybrid populations have been lacking. Here, we develop methods based on the Wavelet Transform to understand the spatial genomic scale of local ancestry variation and its association with recombination rates. We present theory and use simulations to show how wavelet-based decompositions of ancestry variance along the genome and the correlation between ancestry and recombination reflect the joint effects of recombination, genetic drift, and genome-wide selection against introgressed alleles. Due to the clock-like effect of recombination in hybrids breaking up parental haplotypes, drift and selection produce predictable patterns of local ancestry variation at varying spatial genomic scales through time. Using wavelet approaches to identify the genomic scale of variance in ancestry and its correlates, we show that these methods can detect temporally localized effects of drift and selection. We apply these methods to previously published datasets from hybrid populations of swordtail fish (Xiphophorus) and baboons (Papio), and to inferred Neanderthal introgression in modern humans. Across systems, we find that upwards of 20% of the variation in local ancestry at the broadest genomic scales can be attributed to systematic selection against introgressed alleles, consistent with strong selection acting on early-generation hybrids. We also see signals of selection at fine genomic scales and much longer time scales. However, we show that our ability to confidently infer selection at fine scales is likely limited by inherent biases in current methods for estimating local ancestry from genomic similarity. Wavelet approaches will become widely applicable as genomic data from systems with introgression become increasingly available, and can help shed light on generalities of the genomic consequences of interspecific hybridization.