We present T-PHOT, a publicly available software aimed at extracting accurate photometry from low-resolution images of deep extragalactic fields, where the blending of sources can be a serious problem for the accurate and unbiased measurement of fluxes and colours. T-PHOT has been developed within the ASTRODEEP project and it can be considered as the next generation to TFIT, providing significant improvements above it and other similar codes. T-PHOT gathers data from a high-resolution image of a region of the sky, and uses it to obtain priors for the photometric analysis of a lower resolution image of the same field. It can handle different types of datasets as input priors: i) a list of objects that will be used to obtain cutouts from the real high-resolution image; ii) a set of analytical models; iii) a list of unresolved, point-like sources, useful e.g. for far-infrared wavelength domains. We show that T-PHOT yields accurate estimations of fluxes within the intrinsic uncertainties of the method, when systematic errors are taken into account (which can be done thanks to a flagging code given in the output). T-PHOT is many times faster than similar codes like TFIT and CONVPHOT (up to hundreds, depending on the problem and the method adopted), whilst at the same time being more robust and more versatile. This makes it an optimal choice for the analysis of large datasets. In addition we show how the use of different settings and methods significantly enhances the performance. Given its versatility and robustness, T-PHOT can be considered the preferred choice for combined photometric analysis of current and forthcoming extragalactic optical to far-infrared imaging surveys. [abridged]

23 pages, 20 figures, 2 tables