We present the first high spatial resolution radio continuum survey of the southern Galactic plane. The CORNISH project has mapped the region defined by 295{deg}<l<350{deg}; |b|<1{deg} at 5.5-GHz, with a resolution of 2.5" (FWHM). As with the CORNISH-North survey, this is designed to primarily provide matching radio data to the Spitzer GLIMPSE survey region. The CORNISH-South survey achieved a root mean square noise level of ~0.11mJy/beam, using the 6A configuration of the Australia Telescope Compact Array (ATCA). In this paper, we discuss the observations, data processing and measurements of the source properties. Above a 7{sigma} detection limit, 4701 sources were detected, and their ensemble properties show similar distributions with their northern counterparts. The catalogue is highly reliable and is complete to 90 per cent at a flux density level of 1.1mJy. We developed a new way of measuring the integrated flux densities and angular sizes of non-Gaussian sources. The catalogue primarily provides positions, flux density measurements and angular sizes. All sources with IR counterparts at 8{mu}m have been visually classified, utilizing additional imaging data from optical, near-IR, mid-IR, far-IR and sub-millimetre galactic plane surveys. This has resulted in the detection of 524 HII regions of which 255 are ultra-compact HII regions, 287 planetary nebulae, 79 radio stars and 6 massive young stellar objects. The rest of the sources are likely to be extra-galactic. These data are particularly important in the characterization and population studies of compact ionized sources such as UCHII regions and PNe towards the Galactic mid-plane.