Influenza vaccines that confer broad and durable protection against diverse viral strains would have a major effect on global health, as they would lessen the need for annual vaccine reformulation and immunization. Here we show that computationally designed, two-component nanoparticle immunogens induce potently neutralizing and broadly protective antibody responses against a wide variety of influenza viruses. The nanoparticle immunogens contain 20 haemagglutinin glycoprotein trimers in an ordered array, and their assembly in vitro enables the precisely controlled co-display of multiple distinct haemagglutinin proteins in defined ratios. Nanoparticle immunogens that co-display the four haemagglutinins of licensed quadrivalent influenza vaccines elicited antibody responses in several animal models against vaccine-matched strains that were equivalent to or better than commercial quadrivalent influenza vaccines, and simultaneously induced broadly protective antibody responses to heterologous viruses by targeting the subdominant yet conserved haemagglutinin stem. The combination of potent receptor-blocking and cross-reactive stem-directed antibodies induced by the nanoparticle immunogens makes them attractive candidates for a supraseasonal influenza vaccine candidate with the potential to replace conventional seasonal vaccines.