Linguistic processes in the bilingual brain are partially shared across languages, and the degree of neural overlap between the languages is influenced by several factors, including the age of acquisition, relative language proficiency, and immersion. There is limited evidence on the role of linguistic distance on the performance of the language control as well as domain-general cognitive control systems. The present study aims at exploring whether being bilingual in close and distant language pairs (CLP and DLP) influences language control and domain-general cognitive processes. We recruited two groups of DLP (Persian–English) and CLP (French–English) bilinguals. Subjects performed language nonswitching and switching picture-naming tasks and a nonlinguistic switching task while EEG data were recorded. Behaviorally, CLP bilinguals showed a lower cognitive cost than DLP bilinguals, reflected in faster reaction times both in language switching (compared to nonswitching) and nonlinguistic switching. ERPs showed differential involvement of cognitive control regions between the CLP and DLP groups during linguistic switching vs. nonswitching at 450 to 515 ms poststimulus presentation. Moreover, there was a difference between CLP and DLP groups from 40 to 150 ms in the nonlinguistic task. Our electrophysiological results confirm a stronger involvement of language control and domain-general cognitive control regions in CLP bilinguals.