Abstract: On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0 × 10⁻²¹. It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1 σ. The source lies at a luminosity distance of 410/+160/−180/ Mpc corresponding to a redshift z=0.09/+0.03/−0.04/. In the source frame, the initial black hole masses are 36/+5/−4/ M_⊙ and 29/+4/−4/ M_⊙, and the final black hole mass is 62/+4/−4/ M_⊙, with 3.0/+0.5/−0.5/ M_⊙c² radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.