The Amazon rainforest is threatened by land-use change and increasing drought and fire frequency. Studies suggest an abrupt dieback of large parts of the rainforest after partial forest loss, but the critical threshold, underlying mechanisms, and possible impacts of forest degradation on the monsoon circulation remain uncertain. Here, we use a nonlinear dynamical model of the moisture transport and recycling across the Amazon to identify several precursor signals for a critical transition in the coupled atmosphere-vegetation dynamics. Guided by our simulations, we reveal both statistical and physical precursor signals of an approaching critical transition in reanalysis and observational data. In accordance with our model results, we attribute these characteristic precursor signals to the nearing of a critical transition of the coupled Amazon atmosphere-vegetation system induced by forest loss due to deforestation, droughts, and fires. The transition would lead to substantially drier conditions, under which the rainforest could likely not be maintained.