Recycling of spent lithium-ion batteries is important due to the increasing demand for electric vehicles and efforts to realize a circular economy. There is a need to develop environmentally friendly processes for the refining of nickel, cobalt, and other metals contained in the batteries. Electrodialysis is an appealing method for recycling of battery metals with selective separation and low chemical input. In this study, sodium sulfate was used in an electrodialysis metathesis procedure to sequentially separate EDTA-chelated nickel and cobalt. Replacing hitherto used sulfuric acid with sodium sulfate mitigates membrane fouling caused by precipitation of EDTA. It was possible to separate up to 97.9% of nickel and 96.6% of cobalt at 0.10 M, a 30-times higher concentration than previously reported for electrodialysis of similar solutions. Through the thermally activated persulfate method, new to this application, 99.7% of nickel and 87.0% of cobalt could be precipitated from their EDTA chelates. Impurity behavior during electrodialysis of battery leachates has not previously been described in the literature. It is paramount to remove copper, iron, and phosphorous prior to electrodialysis since they contaminate the nickel product. Aluminum was difficult to remove in the solution purification step and ended up in all electrodialysis products.