A general, twisted and tilted, grain boundary in copper has been simulated using the adaptive kinetic Monte Carlo method to study the atomistic structure of the non-crystalline region and the mechanism of annealing events that occur at low temperature. The simulated time interval spanned 67 μs at 135 K. Similar final configurations were obtained starting from different initial structures: (i) by bringing the two grains into contact without any intermediate layer, and (ii) by inserting an amorphous region between the grains. The results obtained were analyzed with a radial distribution function and a common neighbor analysis. Annealing events leading to lowering of the energy typically involved concerted displacement of several atoms—even as many as 10 atoms displaced by more than half an Ångström. Increased local icosahedral ordering is observed in the boundary layer, but local HCP coordination was also observed. In the final low-energy configurations, the thickness of the region separating the crystalline grains corresponds to just one atomic layer, in good agreement with reported experimental observations. The simulated system consists of 1307 atoms and atomic interactions were described using effective medium theory.