The merger of two massive 30 Msun black holes has been detected in gravitational waves (1,GW150914). This discovery validates recent predictions (2-4) that massive binary black holes would constitute the first detection. However, previous calculations have not sampled the relevant binary black hole progenitors---massive, low-metallicity binary stars---with sufficient accuracy and input physics to enable robust predictions to better than several orders of magnitude (5-10). Here we report a suite of high-precision numerical simulations of binary black hole formation via the evolution of isolated binary stars, providing a framework to interpret GW150914 and predict the properties of subsequent binary black hole gravitational-wave events. Our models imply that these events form in an environment where the metallicity is less than 10 percent of solar; have initial masses of 40-100 Msun; and interact through mass transfer and a common envelope phase. Their progenitors likely form either at 2 Gyr, or somewhat less likely, at 11 Gyr after the Big Bang. Most binary black holes form without supernova explosions, and their spins are nearly unchanged since birth, but do not have to be parallel. The classical field formation of binary black holes proposed in this study, with low natal kicks and restricted common envelope evolution, produces 40 times more binary black holes than dynamical formation channels involving globular clusters (11) and is comparable to the rate from homogeneous evolution channels (12-15). Our calculations predict detections of about 1,000 black hole mergers per year with total mass of 20-80 Msun once second generation ground-based gravitational wave observatories reach full sensitivity.