The high sensitivity of tropical hydro-climate to the mean position of the intertropical convergence zone (ITCZ) at different time scales is well known. However, recent research suggests a more complex behaviour of the northern hemispheric tropical rain belts in the western tropical Atlantic. Here we present a precisely dated speleothem multi-proxy record from a well-monitored cave from Puerto Rico, covering the period between 46.2 and 15.4 ka BP in unprecedented resolution. This allows the investigation of multi-decadal to millennial-scale climate variability. The proxy records document a pronounced response of regional rainfall to abrupt centennial to millennial-scale climatic excursions in the North Atlantic across the Last Glacial (i.e., Heinrich Stadials and Dansgaard/Oeschger events). In particular, we observe a strong agreement between the speleothem proxy data and the strength of the Atlantic meridional overturning circulation, supporting a persistent link of regional precipitation to oceanic forcing. Spectral analysis suggests that multi-decadal to centennial variability persisted in the regional hydro-climate not only during stadial and interstadial conditions, but also during the Last Glacial Maximum, supporting the hypothesis that the Atlantic low-latitude regions respond to internal modes of climate variability on these time scales regardless of the global climate state. The compilation with other paleo-precipitation records enables the reconstruction of past changes in position, strength and extent of the ITCZ in the western tropical Atlantic in response to millennial and orbital global climate change.