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. Mechanical cues from the local cellular microenvironment can direct cell fate. Now, experiments with human mesenchymal stem cells cultured on phototunable soft poly(ethylene glycol) hydrogels show that the cells remember past physical environments—with the transcriptional co-activators YAP and TAZ acting as a mechanical rheostat—and therefore that appropriate doses of mechanical cues can be used to manipulate the cells’ fate.