Presented are integrated electrical interconnect board (ICB) assemblies for battery modules, rechargeable traction battery packs equipped with such ICB assemblies, and methods for making/using such ICB assemblies. A battery module for storing and supplying electrical energy includes multiple battery cells that are stacked in side-by-side facing relation with one another and each has a battery cell casing with an electrical terminal projecting therefrom. An electrically insulating module housing has a housing base that supports thereon the stacked battery cells. An integrated ICB assembly, which is attached to the module housing, includes a central cover in spaced facing relation to the housing base, endwalls projecting from the central cover, and multiple busbar connectors attached to the endwalls and electrically connected to the battery cells' electrical terminals. Each endwall has multiple elongated slots that extend from a distal edge of the endwall and slidably receives therethrough one of the electrical terminals.