We present a collection of 250 anomalous Cepheids (ACs) discovered in the OGLE-IV fields toward the Large (LMC) and Small Magellanic Cloud (SMC). The LMC sample is an extension of the OGLE-III Catalog of ACs published in 2008, while the SMC sample contains the first known bona fide ACs in this galaxy. The total sample is composed of 141 ACs in the LMC and 109 ACs in the SMC. All these stars pulsate in single modes: fundamental (174 objects) or first overtone (76 objects). Additionally, we report the discovery of four ACs located in the foreground of the Magellanic Clouds. These are the first unambiguously identified fundamental-mode ACs known in the Galactic field. We demonstrate that the coefficients {phi}21 and {phi}31 determined by the Fourier light curve decomposition are useful discriminators between classical Cepheids and ACs, at least in the LMC and in the field of the Milky Way. In the SMC, the light curve shapes and mean magnitudes of short-period classical Cepheids make them similar to ACs, which is a source of difficulties in the discrimination of both classes of pulsators. The presence of unidentified ACs in the catalogs of classical Cepheids may be partly responsible for the observed non-linearity of the period-luminosity relation observed for short-period Cepheids in the SMC. We compare spatial distributions of ACs, classical Cepheids and RR Lyr stars. We show that the distribution of ACs resembles that of old stars (RR Lyr variables), although in the LMC there are visible structures typical for young population (classical Cepheids): the bar and spiral arms. This may suggest that ACs are a mixture of relatively young stars and mergers of very old stars.