Increasing cell size drives changes to the proteome, which affects cell physiology. As cell size increases, some proteins become more concentrated while others are diluted. As a result, the state of the cell changes continuously with increasing size. In addition to these proteomic changes, large cells have a lower growth rate (protein synthesis rate per unit volume). That both the cell’s proteome and growth rate change with cell size suggests they may be interdependent. To test this, we used quantitative mass spectrometry to measure how the proteome changes in response to the mTOR inhibitor rapamycin, which decreases the cellular growth rate and has only a minimal effect on cell size. We found that large cell size and mTOR inhibition, both of which lower the growth rate of a cell, remodel the proteome in similar ways. This suggests that many of the effects of cell size are mediated by the size-dependent slowdown of the cellular growth rate. For example, the previously reported size-dependent expression of some senescence markers could reflect a cell’s declining growth rate rather than its size per se. In contrast, histones and other chromatin components are diluted in large cells independently of the growth rate, likely so that they remain in proportion with the genome. Finally, size-dependent changes to the cell’s growth rate and proteome composition are still apparent in cells continually exposed to a saturating dose of rapamycin, which indicates that cell size can affect the proteome independently of mTORC1 signaling. Taken together, our results clarify the dependencies between cell size, growth, mTOR activity, and the proteome remodeling that ultimately controls many aspects of cell physiology.