We present the design and first results of a real-time search for transients within the 650 sq. deg. area around the Magellanic Clouds, conducted as part of the OGLE-IV project and aimed at detecting supernovae, novae and other events. The average sampling of about 4 days from September to May, yielded a detection of 238 transients in 2012/2013 and 2013/2014 seasons. The superb photometric and astrometric quality of the OGLE data allows for numerous applications of the discovered transients. We use this sample to prepare and train a Machine Learning-based automated classifier for early light curves, which distinguishes major classes of transients with more than 80% of correct answers. Spectroscopically classified 49 supernovae Type Ia are used to construct a Hubble Diagram with statistical scatter of about 0.3 mag and fill the least populated region of the redshifts range in the Union sample. We investigate the influence of host galaxy environments on supernovae statistics and find the mean host extinction of A_I=0.19+-0.10 mag and A_V=0.39+-0.21 mag based on a subsample of supernovae Type Ia. We show that the positional accuracy of the survey is of the order of 0.5 pixels (0.13 arcsec) and that the OGLE-IV Transient Detection System is capable of detecting transients within the nuclei of galaxies. We present a few interesting cases of nuclear transients of unknown type. All data on the OGLE transients are made publicly available to the astronomical community via the OGLE website.
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