Annually laminated speleothems have the potential to provide information on high-frequency climate variability and, simultaneously, provide good chronological constraints. However, there are distinct types of speleothem annual laminae, from physical to chemical, and a common mechanism that links their formation has yet to be found. Here, we analyzed annually laminated stalagmites from 23 caves and 6 continents with the aim to find if there are common mechanisms underlying their development. Annually laminated stalagmites are least common in arid and semiarid climates, and most common in regions with a seasonality of precipitation. At a global scale, we observe faster growth rates with increasing mean annual temperature and decreasing latitude. Changepoints in average growth rates are infrequent and age-depth relationships demonstrate that growth rates can be approximated to be constant. In general, annually laminated stalagmites are characterized by centennial-scale stability in calcite precipitation due to a sufficiently large and well-mixed water source, a time series spectrum showing first-order autoregression due to mixing of stored water and annual recharged water, and an inter-annual flickering of growth acceleration, bringing growth rates back to the long-term mean. Climate forcing of growth rate variations is observed where a multi-year climate signal is strong enough to be the dominant control on calcite growth rate variability, such that it retains a climate imprint after smoothing of this signal by mixing of stored water. In contrast, long-term constant growth rate of laminated stalagmites adds further robustness to their unparalleled capacity to improve accuracy of chronology building.