We analyze quantum Monte Carlo data in the vicinity of the quantum transition between a Néel state and a quantum paramagnet in a two-layer, square-lattice spin-1/2 Heisenberg antiferromagnet. The real-space correlation function and the universal amplitude ratio of the structure factor and the dynamic susceptibility show clear evidence of quantum critical behavior at low temperatures. The numerical results are in good quantitative agreement with 1/N calculations for the O(N) nonlinear σ model. A discrepancy, reported earlier, between the critical properties of the antiferromagnet and the σ model is resolved. We also discuss the values of prefactors of the dynamic susceptibility and the structure factor in a single-layer antiferromagnet at low T.