Hybrid electrical energy storage (HEES) systems are composed of multiple banks of heterogeneous electrical energy storage (EES) elements with distinctive properties. Charge replacement in a HEES system (i.e., dynamic assignment of load demands to EES banks) is one of the key operations in the system. This paper formally describes the global charge replacement (GCR) optimization problem and provides an algorithm to find the near-optimal GCR control policy. The optimization problem is formulated as a mixed-integer nonlinear programming problem, where the objective function is the charge replacement efficiency. The constraints account for the energy conservation law, efficiency of the charger/converter, the rate capacity effect, and self-discharge rates plus internal resistances of the EES element arrays. The near-optimal solution to this problem is obtained while considering the state of charges (SoCs) of the EES element arrays, characteristics of the load devices, and estimates of energy contributions by the EES element arrays. Experimental results demonstrate significant improvements in the charge replacement efficiency in an example HEES system comprised of banks of battery and supercapacitor elements with a high-power pulsed military radio transceiver as the load device.