Seasonal and year-to-year variations in leaf cover imprint significant spatial and temporal variability on biogeochemical cycles, and affect land-surface properties related to climate. We develop a demographic model of leaf phenology based on the hypothesis that trees seek an optimal Leaf Area Index (LAI) as a function of available light and soil water, and fitted it to spaceborne observations of LAI over the Amazon Basin, 2001–2005. We find the model reproduces the spatial and temporal LAI distribution whilst also predicting geographic variation in leaf age from the basin center (2.1 ± 0.2 yr), through to the lowest values over the deciduous Eastern Amazon (6 ± 2 months). The model explains the observed increase in LAI during the dry season as a net addition of leaves in response to increased solar radiation. We anticipate our work to be a starting point from which to develop better descriptions of leaf phenology to incorporate into more sophisticated earth system models.