We present the morphological catalogue of galaxies in nearby clusters of the WIde-field Nearby Galaxy-clusters Survey (WINGS). The catalogue contains a total number of 39 923 galaxies, for which we provide the automated estimates of the morphological type, applying the purposely devised tool MORPHOT to the V-band WINGS imaging. For ∼3000 galaxies we also provide visual estimates of the morphological type. A substantial part of the paper is devoted to the description of the MORPHOT tool, whose application is limited, at least for the moment, to the WINGS imaging only. The approach of the tool to the automation of morphological classification is a non-parametric and fully empirical one. In particular, MORPHOT exploits 21 morphological diagnostics, directly and easily computable from the galaxy image, to provide two independent classifications: one based on a maximum likelihood (ML), semi-analytical technique and the other one on a neural network (NN) machine. A suitably selected sample of ∼1000 visually classified WINGS galaxies is used to calibrate the diagnostics for the ML estimator and as a training set in the NN machine. The final morphological estimator combines the two techniques and proves to be effective both when applied to an additional test sample of ∼1000 visually classified WINGS galaxies and when compared with small samples of Sloan Digital Sky Survey (SDSS) galaxies visually classified by Fukugita et al. and Nair et al. Finally, besides the galaxy morphology distribution (corrected for field contamination) in the WINGS clusters, we present the ellipticity (ɛ), colour (B−V) and Sersic index (n) distributions for different morphological types, as well as the morphological fractions as a function of the clustercentric distance (in units of R200).