Nervous system enables flexible and adaptive control of behavior, allowing us to modify actions according to task demands. The associated neural population activity is often characterized by low-dimensional manifolds, orthogonal null and potent spaces, and rotations in neural trajectories. These features are conceptualized as “factors” or “latent dynamics” underlying movement preparation and execution, yet their origin and role in movement flexibility remain unclear. Current research attributes these factors to neural networks trained on specific tasks. However, unlike humans, these networks lack the flexibility to changes in task structure without training on excessive data. Additionally, the nonlinear properties of neural networks make their solutions difficult to interpret. Here, we show that neural factors across sensorimotor tasks naturally emerge from optimal control of a linear system composed of a random network coupled to a biomechanical plant. This control scheme replicates key features of population-level factors observed in the motor cortex in center-out reaching tasks, without requiring data-driven optimization. Testing this model on other tasks revealed that the network achieves control by rerouting sensory information and efficiently coupling network nodes within the controller as a function of task parameters. We demonstrate these general principles in selected benchmark tasks that demand flexibility to changing biomechanics (e.g., force fields, inertial loading) and task instructions (e.g., shooting, target redundancy). Although random networks typically exhibit high-dimensional structural rank, our control scheme generates behavior-relevant factors through a simple mechanism: the addition of task-dependent, low-rank input to the network from feedback about the body state. Additionally, the control scheme predicts scaling of population-level factors with behavioral task parameters, a finding supported by simulations and empirical studies in both output-null and output-potent dimensions. Overall, our study provides an interpretable framework linking population activity to behavior, and proposes a candidate mechanism for how flexible control policies emerge in biological neural networks.