We report on the detection of very-high energy ( VHE , E > 100 GeV ) \gamma -ray emission from NGC 1275 , the central radio galaxy of the Perseus cluster of galaxies . The source has been detected by the MAGIC telescopes with a statistical significance of 6.6 ~ { } \sigma above 100 GeV in 46 hr of stereo observations carried out between August 2010 and February 2011 . The measured differential energy spectrum between 70 GeV and 500 GeV can be described by a power law with a steep spectral index of \Gamma = -4.1 \pm 0.7 _ { stat } \pm 0.3 _ { syst } , and the average flux above 100 GeV is F _ { \gamma } = ( 1.3 \pm 0.2 _ { stat } \pm 0.3 _ { syst } ) \times 10 ^ { -11 } ~ { } \mathrm { cm ^ { -2 } ~% { } s ^ { -1 } } . These results , combined with the power-law spectrum measured in the first two years of observations by the Fermi –LAT above 100 MeV , with a spectral index of \Gamma \simeq - 2.1 , strongly suggest the presence of a break or cut-off around tens of GeV in the NGC 1275 spectrum . The light curve of the source above 100 GeV does not show hints of variability on a month time scale . Finally , we report on the nondetection in the present data of the radio galaxy IC 310 , previously discovered by the Fermi –LAT and MAGIC . The derived flux upper limit F ^ { U . L . } _ { \gamma } ( > 300 ~ { } \mathrm { GeV } ) = 1.2 \times 10 ^ { -12 } ~ { } \mathrm { cm ^ { -2 } ~ { } % s ^ { -1 } } is a factor \sim 3 lower than the mean flux measured by MAGIC between October 2009 and February 2010 , thus confirming the year time-scale variability of the source at VHE .