Abstract Permafrost in Arctic floodplains impacts carbon stores, ecosystems, and infrastructure, yet the processes controlling its distribution remain poorly constrained. Here we present a numerical model for the coupled evolution of river meandering and floodplain permafrost that captures the competition between bank erosion and permafrost growth. We show that permafrost extent reaches a dynamic equilibrium in which removal by channel migration is balanced by epigenetic permafrost generation on newly deposited land. This behavior collapses onto a regime space defined by two dimensionless ratios—the rate of bank thaw relative to sediment entrainment and the timescale of permafrost growth relative to meander‐bend cutoff—which organizes three emergent regimes: permafrost‐bounded, confined, and alluvial meanders. Rivers in the confined regime are most sensitive to warming, in which modest increases in bank thaw rates or the permafrost‐growth timescale produce large increases in migration rates and substantial permafrost loss.