The mechanics of the actin cytoskeleton regulates cell morphogenesis during essential physiological processes. While cellular contractility is known to be largely RhoA-dependent, the process by which localized biochemical signals are translated into cell-level responses is not well understood. Here we combine optogenetic control of RhoA in space and time, live cell imaging and traction force microscopy to investigate the dynamics of actomyosin-based force generation in adherent fibroblasts. Local activation of RhoA not only stimulates local recruitment of actin and myosin, but also leads to increased traction forces outside the activation region that rapidly propagate across the cell via stress fibers and drive actin flow towards the region of heightened RhoA. Surprisingly, the flow reverses direction when local RhoA activation stops. We identify zyxin as a regulator of stress fiber mechanics, as stress fibers are fluid-like without flow reversal in its absence. These experimental data are used to constrain a physical model, which demonstrates that stress fibers are elastic-like, even at time scales exceeding turnover of constituent proteins. Such molecular control of actin mechanics likely plays critical roles in regulation of morphogenic events.