Neutrinoless double beta decay is a process that violates lepton number conservation. It is predicted to occur in extensions of the standard model of particle physics. This Letter reports the results from phase I of the Germanium Detector Array (GERDA) experiment at the Gran Sasso Laboratory (Italy) searching for neutrinoless double beta decay of the isotope Ge76. Data considered in the present analysis have been collected between November 2011 and May 2013 with a total exposure of 21.6 kg yr. A blind analysis is performed. The background index is about 1×10−2 counts/(keV kg yr) after pulse shape discrimination. No signal is observed and a lower limit is derived for the half-life of neutrinoless double beta decay of Ge76, T0ν1/2>2.1×1025 yr (90% C.L.). The combination with the results from the previous experiments with Ge76 yields T0ν1/2>3.0×1025 yr (90% C.L.).