Using the StarTrack binary population synthesis code we model the population of double neutron stars in the Galaxy. We include a detailed treatment of the spin evolution of each pulsar due to processes such as spin-down and spin-up during accretion events as well as magnetic field decay. We also model the spatial distribution of double neutron stars by including their natal kicks and subsequent propagation in the Galactic gravitational potential. This synthetic pulsar population is compared to the observed sample of double neutron stars taking into account the selection effects of detection in the radio band, to determine the most likely evolutionary parameters. With these parameters we determine the properties of the double neutron star binaries detectable in gravitational waves by the high-frequency interferometers LIGO and VIRGO. In particular, we discuss the distributions of chirp masses and mass ratios in samples selected by their radio or gravitational wave emission.