The dissociation energy of H2 represents a benchmark quantity to test the accuracy of first-principles calculations. We present a new measurement of the energy interval between the EF Σ1g+(v=0,N=1) state and the 54p11 Rydberg state of H2. When combined with previously determined intervals, this new measurement leads to an improved value of the dissociation energy D0N=1 of ortho-H2 that has, for the first time, reached a level of uncertainty that is 3 times smaller than the contribution of about 1 MHz resulting from the finite size of the proton. The new result of 35 999.582 834(11) cm-1 is in remarkable agreement with the theoretical result of 35 999.582 820(26) cm-1 obtained in calculations including high-order relativistic and quantum-electrodynamics corrections, as reported in the following Letter [M. Puchalski, J. Komasa, P. Czachorowski, and K. Pachucki, Phys. Rev. Lett. 122, 103003 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103003]. This agreement resolves a recent discrepancy between experiment and theory that had hindered a possible use of the dissociation energy of H2 in the context of the current controversy on the charge radius of the proton.