In this paper we present the WeCAPP catalogue of variable stars found in the bulge of M 31. Observations in the WeCAPP microlensing survey (optical R and I bands) for a period of three years (2000-2003) resulted in a database with unprecedented time coverage for an extragalactic variable star study. We detected 23781 variable sources in a 16.1 arcmin × 16.6 arcmin field centered on the nucleus of M 31. The catalogue of variable stars contains the positions, the periods, and the variation amplitudes in the R and I bands. We classified the variables according to their position in the R-band period-amplitude plane. Three groups can be distinguished; while the first two groups can be mainly associated with Cepheid-like variables (population I Cepheids in group I; type II Cepheids and RV Tauri stars in group II), the third one consists of Long Period Variables (LPVs). We detected 37 RV Tauri stars and 11 RV Tauri candidates, which makes this catalogue one of the largest collections of this class of stars to date. The classification scheme is supported by Fourier decomposition of the light curves. Our data shows a correlation of the low-order Fourier coefficients Φ21 with Φ31 for classical Cepheids, as well as for type II Cepheids and RV Tauri stars. Correlating our sample of variable stars with X-ray based catalogues of Kaaret (2002, ApJ, 578, 114) and Kong et al. (2002, ApJ, 577, 738) results in 23 and 31 coincidences, 8 and 12 of which are M 31 globular clusters. The number density of detected variables is clearly not symmetric, which has to be included in the calculations of the expected microlensing event rate towards M 31. This asymmetry is due to the enhanced extinction in the spiral arms superimposed on the bulge of M 31, which reduces the number of sources to about 60%, if compared to areas of equivalent bulge brightness without enhanced extinction present.