Background: COVID-19 may result in persistent symptoms in the post-acute phase, including cognitive and neurological ones. The aim of this study is to investigate the cognitive and neurological features of patients with a confirmed diagnosis of COVID-19 evaluated in the post-acute phase through a direct neuropsychological evaluation. Methods: Individuals recovering from COVID-19 were assessed in an out-patient practice with a complete neurological evaluation and neuropsychological tests (Mini-Mental State Examination; Rey Auditory Verbal Test, Multiple Feature Target Cancellation Test, Trial Making Test, Digit Span Forward and Backward, and Frontal Assessment Battery). Pre- and post-COVID-19 global and mental health status was assessed along with the history of the acute phase of infection. Post-COVID-19 cognitive status was modeled by combining persistent self-reported COVID-related cognitive symptoms and pathologic neuropsychological tests. Results: A total of 406 individuals (average age 54.5 ± 15.1 years, 45.1% women) were assessed on average at 97.8 ± 48.0 days since symptom onset. Persistent self-reported neurological symptoms were found in the areas of sleep (32%), attention (31%), and memory (22%). The MMSE mean score was 28.6. In total, 84 subjects (20.7%) achieved pathologic neuropsychological test results. A high prevalence of failed tests was found in digit span backward (18.7%), trail making (26.6%), and frontal assessment battery (10.9%). Cognitive status was associated with a number of factors including cardiovascular disease history, persistent fatigue, female sex, age, anxiety, and mental health stress. Conclusion: COVID-19 is capable of eliciting persistent measurable neurocognitive alterations particularly relevant in the areas of attention and working memory. These neurocognitive disorders have been associated with some potentially treatable factors and others that may stratify risk at an early stage.