Binary stellar systems form a large fraction of the Galaxy's stars. They are useful as laboratories for studying the physical processes taking place within stars, and must be correctly taken into account when observations of stars are used to study the structure and evolution of the Galaxy. We present a sample of 12760 well-characterised double-lined spectroscopic binaries that are appropriate for statistical studies of the binary populations. They were detected as SB2s using a t-distributed stochastic neighbour embedding (t-SNE) classification and a cross-correlation analysis of GALAH spectra. This sample consists mostly of dwarfs, with a significant fraction of evolved stars and several dozen members of the giant branch. To compute parameters of the primary and secondary star (Teff[1,2], logg[1,2], [Fe/H], Vr[1,2], vmic[1,2], vbroad[1,2], R[1,2], and E(B-V)), we used a Bayesian approach that includes a parallax prior from Gaia DR2, spectra from GALAH, and apparent magnitudes from APASS, Gaia DR2, 2MASS, and WISE. The derived stellar properties and their distributions show trends that are expected for a population of close binaries (a<10AU) with mass ratios 0.5<=q<=1. The derived metallicity of these binary stars is statistically lower than that of single dwarf stars from the same magnitude-limited sample.