The meiotic chromosome axis plays key roles in meiotic chromosome organization and recombination, yet the underlying protein components of this structure are highly diverged. Here, we show that "axis core proteins" from budding yeast (Red1), mammals (SYCP2/SYCP3), and plants (ASY3/ASY4) are evolutionarily related and play equivalent roles in chromosome axis assembly. We first identify motifs in each complex that recruit meiotic HORMADs, the master regulators of meiotic recombination. We next find that axis core complexes form homotetrameric (Red1) or heterotetrameric (SYCP2:SYCP3 and ASY3:ASY4) coiled-coil assemblies that further oligomerize into micron-length filaments. Thus, the meiotic chromosome axis core in fungi, mammals, and plants shares a common molecular architecture and role in axis assembly and recombination control. We propose that the meiotic chromosome axis self-assembles through cooperative interactions between dynamic DNA loop-extruding cohesin complexes and the filamentous axis core, then serves as a platform for chromosome organization, recombination, and synaptonemal complex assembly.