We have conducted an extensive wide-field imaging survey for Cepheid variables in the Local Group irregular galaxy WLM. From data obtained on 101 nights, we have discovered 60 Cepheids, which include 14 of the 15 Cepheid variables previously detected by Sandage and Carlson. Our Cepheid survey in WLM should be practically complete down to a period of 3 days. Importantly, we have found for the first time a long-period Cepheid (P = 54.2 days) in this galaxy, alleviating the problem that WLM with its many blue, massive stars does not contain Cepheids with periods longer than about 10 days. Our data define tight period-luminosity (PL) relations in V, I, and the reddening-free Wesenheit magnitude WI, which are all extremely well fit by the corresponding slopes of the LMC Cepheid PL relation, suggesting no change of the PL relation slope down to a Cepheid metal abundance of about -1.0 dex, in agreement with other recent studies. We derive a true distance modulus to WLM of 25.144 ± 0.03 (random) ±0.07 (systematic) mag from our data, in good agreement with the earlier 24.92 ± 0.21 mag determination of Lee, Freedman, and Madore from Cepheid variables. The quoted value of the systematic uncertainty does not include the contribution from the LMC distance, which we have assumed to be 18.50 mag, as in the previous papers in our project.