ABSTRACT We estimate the properties of the double neutron star (DNS) population that will be observable by the planned space-based interferometer Laser Interferometer Space Antenna (LISA). By following the gravitational radiation-driven evolution of DNSs generated from rapid population synthesis of massive binary stars, we estimate that around 35 DNSs will accumulate a signal-to-noise ratio above 8 over a 4-yr LISA mission. The observed population mainly comprises Galactic DNSs (94 per cent), but detections in the LMC (5 per cent) and SMC (1 per cent) may also be expected. The median orbital frequency of detected DNSs is expected to be 0.8 mHz, and many of them will be eccentric (median eccentricity of 0.11). LISA is expected to localize these DNSs to a typical angular resolution of 2°. We expect the best-constrained DNSs to have eccentricities known to a few parts in a thousand, chirp masses measured to better than 1 per cent fractional uncertainty, and sky localization at the level of a few arcminutes. The orbital properties will provide insights into DNS progenitors and formation channels. The localizations may allow neutron star natal kick magnitudes to be constrained through the Galactic distribution of DNSs, and make it possible to follow up the sources with radio pulsar searches. LISA is also expected to resolve ∼104 Galactic double white dwarfs, many of which may have binary parameters that resemble DNSs; we discuss how the combined measurement of binary eccentricity, chirp mass, and sky location may aid the identification of a DNS.