3D eukaryotic genome organization provides the structural basis for gene regulation. In Drosophila melanogaster, genome folding is characterized by somatic homolog pairing, where homologous chromosomes are intimately paired from end to end; however, how homologs identify one another and pair has remained mysterious. Recently, this process has been proposed to be driven by specifically interacting 'buttons' encoded along chromosomes. Here, we turned this hypothesis into a quantitative biophysical model to demonstrate that a button-based mechanism can lead to chromosome-wide pairing. We tested our model using live-imaging measurements of chromosomal loci tagged with the MS2 and PP7 nascent RNA labeling systems. We show solid agreement between model predictions and experiments in the pairing dynamics of individual homologous loci. Our results strongly support a button-based mechanism of somatic homolog pairing in Drosophila and provide a theoretical framework for revealing the molecular identity and regulation of buttons.