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We report the INTernational Gamma-ray Astrophysics Laboratory (INTEGRAL) detection of the short gamma-ray burst GRB 170817A (discovered by Fermi-GBM) with a signal-to-noise ratio of 4.6, and, for the first time, its association with the gravitational waves (GWs) from binary neutron star (BNS) merging event GW170817 detected by the LIGO and Virgo observatories. The significance of association between the gamma-ray burst observed by INTEGRAL and GW170817 is 3.2 σ, while the association between the Fermi-GBM and INTEGRAL detections is 4.2 σ. GRB 170817A was detected by the SPI-ACS instrument about 2 s after the end of the GW event. We measure a fluence of (1.4±0.4±0.6)× 10− 7 erg cm− 2 (75–2000 keV), where, respectively, the statistical error is given at the 1σ confidence level, and the systematic error corresponds to the uncertainty in the spectral model and instrument response. We also …