The Murchison Widefield Array ( MWA ) has observed the entire southern sky ( Declination , \delta < 30 ^ { \circ } ) at low radio-frequencies , over the range 72–231 MHz . These observations constitute the GaLactic and Extragalactic All-sky MWA ( GLEAM ) Survey , and we use the extragalactic catalogue ( Galactic latitude , |b| > 10 ^ { \circ } ) to define the GLEAM 4-Jy ( G4Jy ) Sample . This is a complete sample of the ‘ brightest ’ radio-sources ( S _ { \mathrm { 151 MHz } } > 4 Jy ) , the majority of which are active galactic nuclei with powerful radio-jets . Crucially , low-frequency observations allow the selection of such sources in an orientation-independent way ( i.e . minimising the bias caused by Doppler boosting , inherent in high-frequency surveys ) . We then use higher-resolution radio images , and information at other wavelengths , to morphologically classify the brightest components in GLEAM . We also conduct cross-checks against the literature , and perform internal matching , in order to improve sample completeness ( which is estimated to be > 95.5 % ) . This results in a catalogue of 1,863 sources , making the G4Jy Sample over 10 times larger than that of the revised Third Cambridge Catalogue of Radio Sources ( 3CRR ; S _ { \mathrm { 178 MHz } } > 10.9 Jy ) . Of these G4Jy sources , 78 are resolved by the MWA ( Phase-I ) synthesised beam ( \sim 2 ^ { \prime } at 200 MHz ) , and we label 67 % of the sample as ‘ single ’ , 26 % as ‘ double ’ , 4 % as ‘ triple ’ , and 3 % as having ‘ complex ’ morphology at \sim 1 GHz ( 45 ^ { \prime \prime } resolution ) . We characterise the spectral behaviour of these objects in the radio , and find that the median spectral-index is \alpha = -0.740 \pm 0.012 between 151 MHz and 843 MHz , and \alpha = -0.786 \pm 0.006 between 151 MHz and 1400 MHz ( assuming a power-law description , S _ { \nu } \propto \nu ^ { \alpha } ) , compared to \alpha = -0.829 \pm 0.006 within the GLEAM band . Alongside this , our value-added catalogue provides mid-infrared source associations ( subject to 6 ^ { \prime \prime } resolution at 3.4 \mu m ) for the radio emission , as identified through visual inspection and thorough checks against the literature . As such , the G4Jy Sample can be used as a reliable training set for cross-identification via machine-learning algorithms . We also estimate the angular size of the sources , based on their associated components at \sim 1 GHz , and perform a flux-density comparison for 67 G4Jy sources that overlap with 3CRR . Analysis of multi-wavelength data , and spectral curvature between 72 MHz and 20 GHz , will be presented in subsequent papers , and details for accessing all G4Jy overlays are provided at https : //github.com/svw26/G4Jy .