In the classical views of systems memory consolidation, memories are transferred from the hippocampus to cortex. But with the advance of recording techniques, it appears that many memories are learned and represented in multiple brain regions simultaneously. Moreover, representations change dynamically while the behavior of animals remains stable. Here, we propose a population perspective on memory consolidation that reproduces many features of this “representational drift”. We develop an analytically tractable model for the dynamics of memory engrams that is structurally similar to a recurrent neural network (RNN), but operates on the longer time scale of memory consolidation (Fig. 1A). Memories in our model are not transferred between brain regions (Fig. 1B) but rather redistributed across or within regions (Fig. 1C), and remain stable during consolidation by confining the engram dynamics to the null space of a memory readout. The resulting changes in population activity are in agreement with representational drift effects observed in vivo (Fig. 1D). Neuronal tuning curves show a diversity of changes, including stability, gradual drifts in the preferred stimulus, abrupt remapping, and a loss or gain of tuning. Decoders trained on one session show limited generalization over time, while multi-day decoders reveal invariant subspaces in population activity. Finally, our model suggests that engram dynamics driven by consolidation can appear random when recording a subsample of engram neurons (Fig. 1E). In summary, we present a model of memory consolidation which produces highly distributed memory representations, and which allows a new perspective on consolidation as driven by RNN dynamics.