The effects of topological patterning (i.e., grating and rectangular patterns) on the self-rolling behaviors of heteroepitaxial strained nanomembranes have been systematically studied. An analytical modeling framework, validated through finite-element simulations, has been formulated to predict the resultant curvature of the patterned nanomembrane as the pattern thickness and density vary. The effectiveness of the grating pattern in regulating the rolling direction of the nanomembrane has been demonstrated and quantitatively assessed. Further to the rolling of nanomembranes, a route to achieve predictive design of helical structures has been proposed and showcased. The present study provides new knowledge and mechanistic guidance towards predictive control and tuning of roll-up nanostructures via topological patterning.