Background: Balance control is important for mobility, yet exoskeleton research has mainly focused on improving metabolic energy efficiency. Here we present a biomimetic exoskeleton controller that supports walking balance and reduces muscle activity. Methods: Humans restore balance after a perturbation by adjusting activity of the muscles actuating the ankle in proportion to deviations from steady-state center of mass kinematics. We designed a controller that mimics the neural control of steady-state walking and the balance recovery responses to perturbations. This controller uses both feedback from ankle kinematics in accordance with an existing model and feedback from the center of mass velocity. Control parameters were estimated by fitting the experimental relation between kinematics and ankle moments observed in humans that were walking while being perturbed by push and pull perturbations. This identified model was implemented on a bilateral ankle exoskeleton. Results: Across twelve subjects, exoskeleton support reduced calf muscle activity in steady-state walking by 19% with respect to a minimal impedance controller (p < 0.001). Proportional feedback of the center of mass velocity improved balance support after perturbation. Muscle activity is reduced in response to push and pull perturbations by 10% (p = 0.006) and 16% (p < 0.001) and center of mass deviations by 9% (p = 0.026) and 18% (p = 0.002) with respect to the same controller without center of mass feedback. Conclusion: Our control approach implemented on bilateral ankle exoskeletons can thus effectively support steady-state walking and balance control and therefore has the potential to improve mobility in balance-impaired individuals.