Systems consolidation refers to the time-dependent reorganization of memory representations or engrams across brain regions. Despite recent advancements in unravelling this process, the exact mechanisms behind engram dynamics and the role of associated pathways remain largely unknown. Here we propose a biologically-plausible computational model to address this knowledge gap. By coordinating synaptic plasticity timescales and incorporating a hippocampus-thalamus-cortex circuit, our model is able to couple engram reactivations across these regions and thereby reproduce key dynamics of cortical and hippocampal engram cells along with their interdependencies. Decoupling hippocampal-thalamic-cortical activity disrupts systems consolidation. Critically, our model yields testable predictions regarding hippocampal and thalamic engram cells, inhibitory engrams, thalamic inhibitory input, and the effect of thalamocortical synaptic coupling on retrograde amnesia induced by hippocampal lesions. Overall, our results suggest that systems consolidation emerges from coupled reactivations of engram cells in distributed brain regions enabled by coordinated synaptic plasticity timescales in multisynaptic subcortical-cortical circuits.