The successful completion of meiosis is essential for all sexually reproducing organisms. The synaptonemal complex (SC) is a large proteinaceous structure that holds together homologous chromosomes during meiosis, providing the structural framework for meiotic recombination and crossover formation. Errors in SC formation are associated with infertility, recurrent miscarriage and aneuploidy. The current lack of molecular information about the dynamic process of SC assembly severely restricts our understanding of its function in meiosis. Here, we provide the first biochemical and structural analysis of an SC protein component and propose a structural basis for its function in SC assembly. We show that human SC proteins SYCE2 and TEX12 form a highly stable, constitutive complex, and define the regions responsible for their homotypic and heterotypic interactions. Biophysical analysis reveals that the SYCE2–TEX12 complex is an equimolar hetero-octamer, formed from the association of an SYCE2 tetramer and two TEX12 dimers. Electron microscopy shows that biochemically reconstituted SYCE2–TEX12 complexes assemble spontaneously into filamentous structures that resemble the known physical features of the SC central element (CE). Our findings can be combined with existing biological data in a model of chromosome synapsis driven by growth of SYCE2–TEX12 higher-order structures within the CE of the SC.