Context : Millimetre-wave continuum astronomy is today an indispensable tool for both general astrophysics studies ( e.g . star formation , nearby galaxies ) and cosmology ( e.g . CMB - cosmic microwave background and high-redshift galaxies ) . General purpose , large-field-of-view instruments are needed to map the sky at intermediate angular scales not accessible by the high-resolution interferometers ( e.g . ALMA in Chile , NOEMA in the French Alps ) and by the coarse angular resolution space-borne or ground-based surveys ( e.g . Planck , ACT , SPT ) . These instruments have to be installed at the focal plane of the largest single-dish telescopes , which are placed at high altitude on selected dry observing sites . In this context , we have constructed and deployed a three-thousand-pixel dual-band ( 150 GHz and 260 GHz , respectively 2 mm and 1.15 mm wavelengths ) camera to image an instantaneous circular field-of-view of 6.5 arcminutes in diameter , and configurable to map the linear polarisation at 260 GHz . Aims : First , we are providing a detailed description of this instrument , named NIKA2 ( New IRAM KID Arrays 2 ) , in particular focussing on the cryogenics , optics , focal plane arrays based on Kinetic Inductance Detectors ( KID ) , and the readout electronics . The focal planes and part of the optics are cooled down to the nominal 150 mK operating temperature by means of an ad-hoc dilution refrigerator . Secondly , we are presenting the performance measured on the sky during the commissioning runs that took place between October 2015 and April 2017 at the 30-meter IRAM ( Institut of Millimetric Radio Astronomy ) telescope at Pico Veleta , near Granada ( Spain ) . Methods : We have targeted a number of astronomical sources . Starting from beam-maps on primary and secondary calibrators we have then gone to extended sources and faint objects . Both internal ( electronic ) and on-the-sky calibrations are applied . The general methods are described in the present paper . Results : NIKA2 has been successfully deployed and commissioned , performing in-line with expectations . In particular , NIKA2 exhibits full width at half maximum ( FWHM ) angular resolutions of around 11 and 17.5 arc-seconds at respectively 260 and 150 GHz . The noise equivalent flux densities ( NEFD ) are , at these two respective frequencies , 33 \pm 2 and 8 \pm 1 mJy \cdot \textrm { s } ^ { 1 / 2 } . A first successful science verification run was achieved in April 2017 . The instrument is currently offered to the astronomy community and will remain available for at least the following ten years . Conclusions :