We present a VLT/FORS1 survey of Wolf-Rayet (WR) stars in the spiral galaxy NGC 1313. In total, 94 WR candidate sources have been identified from narrow-band imaging. Of these, 82 have been spectroscopically observed, for which WR emission features are confirmed in 70 cases, one of which also exhibits strong nebular HeII{lambda}4686 emission. We also detect strong nebular HeII{lambda}4686 emission within two other regions of NGC 1313, one of which is a possible supernova remnant. Nebular properties confirm that NGC 1313 has a metal content log(O/H)+12=8.23+/-0.06, in good agreement with previous studies. From continuum-subtracted H{alpha} images we infer a global star formation rate of 0.6M_{sun}/yr. Using template LMC WR stars, spectroscopy reveals that NGC 1313 hosts a minimum of 84 WR stars. Our census comprises 51 WN stars, including a rare WN/C transition star plus 32 WC stars. In addition, we identify one WO star which represents the first such case identified beyond the Local Group. The bright giant HII region PES 1, comparable in H{alpha} luminosity to NGC 595 in M 33, is found to host a minimum of 17 WR stars. The remaining photometric candidates generally display photometric properties consistent with WN stars, such that we expect a global WR population of ~115 stars with N(WR)/N(O)~0.01 and N(WC)/N(WN)~0.4.