Many lipid-tethered proteins and glycolipids exist as monomers and nanoclusters on the surface of living cells. The spatial distribution and dynamics of formation and breakup of nanoclusters does not reflect thermal and chemical equilibrium and is controlled by active remodeling of the underlying cortical actin. We propose a model for nanoclustering based on active hydrodynamics, wherein cell surface molecules bound to dynamic actin are actively driven to form transient clusters. This consistently explains all of our experimental observations. Using FCS and TIRF microscopy, we provide evidence for the existence of short, dynamic, polymerizing actin filaments at the cortex, a key assumption of the theoretical framework. Our theory predicts that lipid-anchored proteins that interact with dynamic actin must exhibit anomalous concentration fluctuations, and a cell membrane protein capable of binding directly to actin can form nanoclusters. These we confirm experimentally, providing an active mechanism for molecular organization and its spatiotemporal regulation on the plasma membrane.