The theory of plate tectonics describes how the surface of Earth is split into an organized jigsaw of seven large plates(1) of similar sizes and a population of smaller plates whose areas follow a fractal distribution(2,3). The reconstruction of global tectonics during the past 200 million years(4) suggests that this layout is probably a long-term feature of Earth, but the forces governing it are unknown. Previous studies(3,5,6), primarily based on the statistical properties of plate distributions, were unable to resolve how the size of the plates is determined by the properties of the lithosphere and the underlying mantle convection. Here we demonstrate that the plate layout of Earth is produced by a dynamic feedback between mantle convection and the strength of the lithosphere. Using three-dimensional spherical models of mantle convection that self-consistently produce the plate size-frequency distribution observed for Earth, we show that subduction geometry drives the tectonic fragmentation that generates plates. The spacing between the slabs controls the layout of large plates, and the stresses caused by the bending of trenches break plates into smaller fragments. Our results explain why the fast evolution in small back-arc plates(7,8) reflects the marked changes in plate motions during times of major reorganizations. Our study opens the way to using convection simulations with plate-like behaviour to unravel how global tectonics and mantle convection are dynamically connected.