We have performed an exclusive measurement of the K-+He3→Λpn reaction at an incident kaon momentum of 1GeV/c. In the Λp invariant mass spectrum, a clear peak was observed below the mass threshold of K̄+N+N, as a signal of the kaonic nuclear bound state, K̄NN. The binding energy, decay width, and S-wave Gaussian reaction form factor of this state were observed to be BK=42±3(stat.)-4+3(syst.)MeV, ΓK=100±7(stat.)-9+19(syst.)MeV, and QK=383±11(stat.)-1+4(syst.)MeV/c, respectively. The total production cross section of K̄NN, determined by its Λp decay mode, was σKtotBRΛp=9.3±0.8(stat.)-1.0+1.4(syst.)μb. We estimated the branching ratio of the K̄NN state to the Λp and ς0p decay modes as BRΛp/BRς0p∼1.7, by assuming that the physical processes leading to the ςNN final states are analogous to those of Λpn.