We describe the Herschel Virgo Cluster Survey and the first data that cover the complete survey area (four 4 × 4 deg2 regions). We use these data to measure and compare the global far-infrared properties of 78 optically bright galaxies that are selected at 500 μm and detected in all five far-infrared bands. We show that our measurements and calibration are broadly consistent with previous data obtained by the IRAS, ISO, Spitzer and Planck. We use SPIRE and PACS photometry data to produce 100-, 160-, 250-, 350- and 500-μm cluster luminosity distributions. These luminosity distributions are not power laws, but ‘peaked’, with small numbers of both faint and bright galaxies. We measure a cluster 100–500 μm far-infrared luminosity density of 1.6(7.0) ± 0.2 × 109 L⊙ Mpc−3. This compares to a cluster 0.4–2.5 μm optical luminosity density of 5.0(20.0) × 109 L⊙ Mpc−3, some 3.2(2.9) times larger than the far-infrared. A ‘typical’ photon originates from an optical depth of 0.4 ± 0.1. Most of our sample galaxies are well fitted by a single modified blackbody (β= 2), leading to a mean dust mass of log MDust= 7.31 M⊙ and temperature of 20.0 K. We also derive both stellar and atomic hydrogen masses from which we calculate mean values for the star-to-gas (atomic) and gas (atomic)-to-dust mass ratios of 15.1 and 58.2, respectively. Using our derived dust, atomic gas and stellar masses, we estimate cluster mass densities of 8.6(27.8) × 106, 4.6(13.9) × 108 and 7.8(29.7) × 109 M⊙ Mpc−3 for dust, atomic gas and stars, respectively. These values are higher than those derived for field galaxies by factors of 39(126), 6(18) and 34(129), respectively. In the above, the luminosity/mass densities are given using the whole sample with the values in brackets using just those galaxies that lie between 17 and 23 Mpc. We provide a data table of flux densities in all the Herschel bands for all 78 bright Virgo Cluster galaxies.