We obtain the total impulse in the scattering of nonspinning binaries in general relativity at fourth post-Minkowskian order, i.e., O(G4), including linear, nonlinear, and hereditary radiation-reaction effects. We derive the total radiated spacetime momentum as well as the associated energy flux. The latter can be used to compute gravitational-wave observables for generic (un)bound orbits. We employ the ("in-in") Schwinger-Keldysh worldline effective field theory framework in combination with modern "multiloop"integration techniques from collider physics. The complete results are in agreement with various partial calculations in the post-Minkowskian and post-Newtonian expansion.