Cosmic rays could be produced via shock acceleration powered by supernovae. The supernova hypothesis implies that each supernova injects, on average, some 10^{50} erg in cosmic rays, while the shock acceleration model predicts a power law cosmic ray spectrum with the slope close to 2. Verification of these predictions requires measurement of the spectrum and power of cosmic ray injection from supernova population(s). Here, we obtain such measurements based on γ-ray observation of the Constellation III region of the Large Magellanic Cloud. We show that γ-ray emission from this young star formation region originates from cosmic rays injected by approximately two thousand supernovae, rather than by a massive star wind powered by a superbubble predating supernova activity. Cosmic ray injection power is found to be (1.1_{-0.2}^{+0.5})×10^{50} erg/supernova (for the estimated interstellar medium density 0.3 cm^{-3}). The spectrum is a power law with slope 2.09_{-0.07}^{+0.06}. This agrees with the model of particle acceleration at supernova shocks and provides a direct proof of the supernova origin of cosmic rays.