Context. Gaia is an ESA cornerstone mission launched on 19 December 2013 aiming to obtain the most complete and precise 3D map of our Galaxy by observing more than one billion sources. This paper is part of a series of documents explaining the data processing and its results for Gaia Data Release 1, focussing on the G band photometry. Aims. This paper describes the calibration model of the Gaia photometric passband for Gaia Data Release 1. Methods. The overall principle of splitting the process into internal and external calibrations is outlined. In the internal calibration, a self-consistent photometric system is generated. Then, the external calibration provides the link to the absolute photometric flux scales. Results. The Gaia photometric calibration pipeline explained here was applied to the first data release with good results. Details are given of the various calibration elements including the mathematical formulation of the models used and of the extraction and preparation of the required input parameters (e.g. colour terms). The external calibration in this first release provides the absolute zero point and photometric transformations from the Gaia G passband to other common photometric systems. Conclusions. This paper describes the photometric calibration implemented for the first Gaia data release and the instrumental effects taken into account. For this first release no aperture losses, radiation damage, and other second-order effects have not yet been implemented in the calibration.