There are simple conceptual models of tropical cyclone intensification and potential intensity. However, such a framework has been lacking to describe the evolution of the outer circulation. An analytic growth model of the tropical cyclone outer size is derived from the angular momentum equation. The growth model fits a full-physics idealized tropical cyclone simulation. The lifecycle composite of the best-track outer size growth shows a strong super-linear nature, which supports an exponential growth as predicted by the growth model. The climatology of outer size growth measured by the radius of gale-force wind in the North Atlantic and Eastern Pacific during the period 2004–2017, can be understood in terms of four growth factors of the model: the initial size, the growth duration, the mean growth latitude, and the mean top-of-boundary-layer effective local inflow angle. All four variables are significantly different between the two basins. The observed lifetime maximum size follows a lognormal distribution, which is in line with the law of the proportionate effect of this exponential growth model. The growth model fits the observed outer size well in global basins. The time constant of the exponential size growth is approximately equal to the product of the Coriolis parameter and the mean effective inflow angle above the boundary layer. Further sensitivity experiments with the growth model suggest that the interannual variability of the global lifetime maximum size is largely driven by the variation of growth duration.