Residual stresses are a persistent problem in electrodeposited thin films. Stress can lead to cracking or delamination and limit the performance of protective coatings that are grown by electrodeposition. The deposition conditions can greatly modify the stress, so it would be useful to understand how they effect the stress in order to better predict and control it. Therefore, we have performed systematic experiments to measure the dependence of stress on the growth rate and electrolyte composition in electrodeposited Ni and Cu films. Because the microstructure of the film can change with thickness, we have also characterized the grain size evolution for correlation with the stress. This leads to some surprising behavior. For films that grow with tensile stress (high growth rate), the stress becomes less tensile for larger grain size. For films that grow with compressive stress (low growth rate), the stress becomes less compressive/more tensile for larger grain size. These results are interpreted in terms of a kinetic model that focuses on stress-generating processes occurring at the boundary between adjacent grains as the film grows.