The evolution of cancer genomes within a single tumor creates mixed cell populations with divergent somatic mutational landscapes. Inference of tumor subpopulations has been disproportionately focused on the assessment of somatic point mutations, whereas computational methods targeting evolutionary dynamics of copy number alterations (CNA) and loss of heterozygosity (LOH) in whole-genome sequencing data remain underdeveloped. We present a novel probabilistic model, TITAN, to infer CNA and LOH events while accounting for mixtures of cell populations, thereby estimating the proportion of cells harboring each event. We evaluate TITAN on idealized mixtures, simulating clonal populations from whole-genome sequences taken from genomically heterogeneous ovarian tumor sites collected from the same patient. In addition, we show in 23 whole genomes of breast tumors that the inference of CNA and LOH using TITAN critically informs population structure and the nature of the evolving cancer genome. Finally, we experimentally validated subclonal predictions using fluorescence in situ hybridization (FISH) and single-cell sequencing from an ovarian cancer patient sample, thereby recapitulating the key modeling assumptions of TITAN.