We assessed changes in functional connectivity by fMRI (functional magnetic resonance imaging) and cognitive measures in otherwise neurologically asymptomatic people with HIV (PWH) switching combination antiretroviral therapy (cART). In a prospective study (baseline and follow-up after at least 4 months), virologically suppressed PWH switched non-nuclease reverse-transcriptase inhibitors (NNRTI; tenofovir-DF/emtricitabine with efavirenz to rilpivirine) and integrase-strand-transfer inhibitors (INSTI; tenofovir-DF/emtricitabine with raltegravir to dolutegravir). PWH were assessed by resting-state fMRI and stop-signal reaction time (SSRT) task fMRI as well as with a cognitive battery (CogState™) at baseline and follow-up. Switching from efavirenz to rilpivirine (n = 10) was associated with increased functional connectivity in the dorsal attention network (DAN) and a reduction in SSRTs (p = 0.025) that positively correlated with the time previously on efavirenz (mean = 4.8 years, p = 0.02). Switching from raltegravir to dolutegravir (n = 12) was associated with increased connectivity in the left DAN and bilateral sensory-motor and associative visual networks. In the NNRTI study, significant improvements in the cognitive domains of executive function, working memory and speed of visual processing were observed, whereas no significant changes in cognitive function were observed in the INSTI study. Changes in fMRI are evident in PWH without perceived neuropsychiatric complaints switching cART. fMRI may be a useful tool in assisting to elucidate the underlying pathogenic mechanisms of cART-related neuropsychiatric effects.