We investigated whether stem cells remember past physical signals and whether these can be exploited to dose cells mechanically. We found that the activation of the Yes-associated protein (YAP) and transcriptional coactivator with PDZ-binding domain (TAZ) as well as the pre-osteogenic transcription factor RUNX2 in human mesenchymal stem cells (hMSCs) cultured on soft poly(ethylene glycol) (PEG) hydrogels (Young’s modulus E ~ 2 kPa) depended on previous culture time on stiff tissue culture polystyrene (TCPS; E ~ 3 GPa). In addition, mechanical dosing of hMSCs cultured on initially stiff (E ~ 10 kPa) and then soft (E ~ 2 kPa) phototunable PEG hydrogels resulted in either reversible or—above a threshold mechanical dose—irreversible activation of YAP/TAZ and RUNX2. We also found that increased mechanical dosing on supraphysiologically stiff TCPS biases hMSCs towards osteogenic differentiation. We conclude that stem cells possess mechanical memory—with YAP/TAZ acting as an intracellular mechanical rheostat—that stores information from past physical environments and influences the cells’ fate.