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We present new reddening maps of the SMC and LMC based on the data of thethird phase of the Optical Gravitational Lensing Experiment (OGLE III). We haveused two different methods to derive optical reddening maps. We adopt atheoretical mean unreddened colour for the red clump in the SMC and LMC,respectively. We subdivide the photometric data for both Clouds into subfieldsand calculate the difference between the observed red clump position and thetheoretical value for each field, which provides us with the reddening value in(V-I). Furthermore reddening values are obtained for 13490 LMC RR Lyrae ab and1529 SMC RR Lyrae ab stars covering the whole OGLE III region of the MCs. Theobserved colours (V-I) of the RR Lyrae stars are compared with the colour fromthe absolute magnitudes. The absolute magnitude of each RR Lyrae star iscomputed using its period and metallicity derived from Fourier decomposition ofits lightcurve. In general we find a low and uniform reddening distribution inboth Magellanic Clouds. The red clump method indicates a mean reddening of theLMC of E(V-I) = 0.09 +/- 0.07 mag, while for the SMC E(V-I) = 0.04 +/- 0.06 magis obtained. With RR Lyrae stars a median value of E(V-I) = 0.11 +/- 0.06 magfor the LMC and E(V-I) = 0.07 +/- 0.06 mag for the SMC is found. The LMC showsvery low reddening in the bar region, whereas the reddening in the star-formingleading edge and 30 Doradus is considerably higher. In the SMC three pronouncedregions with higher reddening are visible. Two are located along the bar, whilethe highest reddening is found in the star-forming wing of the SMC. In generalthe regions with higher reddening are in good spatial agreement with infraredreddening maps as well as with reddening estimations of other studies. Theposition-dependent reddening values from the red clump method are available viathe Virtual Observatory interface.

New Optical Reddening Maps of the Large and Small Magellanic Clouds