Regulation of cell proliferation is necessary for immune responses, tissue repair, and upkeep of organ function to maintain human health(1). When proliferating cells complete mitosis, a fraction of newly born daughter cells immediately enter the next cell cycle, while the remaining cells in the same population exit to a transient or persistent quiescent state(2). Whether this choice between two cell-cycle pathways is due to natural variability in mitogen signalling or other underlying causes is unknown. Here we show that human cells make this fundamental cell-cycle entry or exit decision based on competing memories of variable mitogen and stress signals. Rather than erasing their signalling history at cell-cycle checkpoints before mitosis, mother cells transmit DNA damage-induced p53 protein and mitogen-induced cyclin D1 (CCND1) mRNA to newly born daughter cells. After mitosis, the transferred CCND1 mRNA and p53 protein induce variable expression of cyclin D1 and the CDK inhibitor p21 that almost exclusively determines cell-cycle commitment in daughter cells. We find that stoichiometric inhibition of cyclin D1-CDK4 activity by p21 controls the retinoblastoma (Rb) and E2F transcription program in an ultrasensitive manner. Thus, daughter cells control the proliferation-quiescence decision by converting the memories of variable mitogen and stress signals into a competition between cyclin D1 and p21 expression. We propose a cell-cycle control principle based on natural variation, memory and competition that maximizes the health of growing cell populations.