We have obtained multi-epoch, high-resolution spectroscopy of 218 candidate low-mass stars and brown dwarfs (BDs) in the young clusters around {lambda} Ori and {sigma} Ori. We find that 196 targets are cluster members based on their radial velocity, the equivalent width of their NaI 8200 lines and the spectral type from their TiO band strength. We have identified 11 new binary stars among the cluster members based on their variable radial velocity and an additional binary from the variation in its linewidth and shape. Of these, six are double-lined spectroscopic binaries (SB2) where the components of the binary are of comparable brightness. The others are single-lined binaries (SB1) in which the companion is faint or the spectra of the stars are blended. There are three narrow-lined SB1 binaries in our sample for which the companion is more than 2.5mag fainter than the primary.