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We report the results of deep optical follow-up surveys of the first twogravitational-wave sources, GW150914 and GW151226, done by the GRAvitationalWave Inaf TeAm Collaboration (GRAWITA). The VLT Survey Telescope (VST)responded promptly to the gravitational-wave alerts sent by the LIGO and VirgoCollaborations, monitoring a region of $90$ deg$^2$ and $72$ deg$^2$ forGW150914 and GW151226, respectively, and repeated the observations over nearlytwo months. Both surveys reached an average limiting magnitude of about 21 inthe $r-$band. The paper describes the VST observational strategy and twoindependent procedures developed to search for transient counterpart candidatesin multi-epoch VST images. Several transients have been discovered but nocandidates are recognized to be related to the gravitational-wave events.Interestingly, among many contaminant supernovae, we find a possiblecorrelation between the supernova VSTJ57.77559-59.13990 and GRB150827A detectedby {\it Fermi}-GBM. The detection efficiency of VST observations for differenttypes of electromagnetic counterparts of gravitational-wave events areevaluated for the present and future follow-up surveys.

GRAWITA: VLT Survey Telescope observations of the gravitational wave sources GW150914 and GW151226