The first observational run of the Advanced LIGO detectors, from September 12, 2015 to January 19,2016, saw the first detections of gravitational waves from binary black hole mergers. In this paper, wepresent full results from a search for binary black hole merger signals with total masses up to 100M⊙ anddetailed implications from our observations of these systems. Our search, based on general-relativisticmodels of gravitational-wave signals from binary black hole systems, unambiguously identified twosignals, GW150914 and GW151226, with a significance of greater than 5σ over the observing period. Italso identified a third possible signal, LVT151012, with substantially lower significance and with an 87%probability of being of astrophysical origin. We provide detailed estimates of the parameters of theobserved systems. Both GW150914 and GW151226 provide an unprecedented opportunity to study thetwo-body motion of a compact-object binary in the large velocity, highly nonlinear regime. We do notobserve any deviations from general relativity, and we place improved empirical bounds on several highorderpost-Newtonian coefficients. From our observations, we infer stellar-mass binary black hole mergerrates lying in the range 9–240 Gpc−3 yr−1. These observations are beginning to inform astrophysicalpredictions of binary black hole formation rates and indicate that future observing runs of the Advanceddetector network will yield many more gravitational-wave detections.