Background/Objectives: Olfactory dysfunction (OD) is associated with a variety of neurologic deficits and impacts socialization decisions, mood, and overall quality of life. As a common symptom comprising the long COVID condition, persistent COVID-19-associated olfactory dysfunction (C19OD) may further impact the presentations of neuropsychiatric sequelae. Our study aims to characterize the longitudinal burden of depression, anxiety, and neuropsychiatric symptoms in a population with C19OD. Methods: Individuals with perceived C19OD completed a psychophysical screening evaluation of their sense of smell using the comprehensive Sniffin’ Sticks olfactory assessment. Only those with validated psychophysical OD were included in this prospective longitudinal study for baseline and one-year follow-up. Participants also completed PHQ-9, Beck Anxiety Inventory (BAI), and neuropsychiatric symptom questionnaires at each time point. Anxiety, depression, and neuropsychiatric symptom prevalence was calculated and compared between time points with Pearson’s chi-squared, Fisher’s exact, and Wilcoxon rank sum tests. Results: Each neuropsychiatric symptom evaluated in this study was reported by 13–49% of longitudinal cohort participants at both baseline and follow-up, except for seizure (0% at baseline and follow-up) and word-finding difficulty (61–68% at baseline and follow-up). Word-finding and focus difficulties were the most commonly reported symptoms. In total, 41% of participants reported some level of depression at baseline and 38% of participants reported depression at one-year follow-up, while 29% and 27% of participants reported some level of anxiety at respective time points. Conclusions: Individuals with C19OD are at risk for developing persistent neuropsychiatric conditions. These neurologic and psychiatric sequelae are persistent with repeated longitudinal assessment, even at nearly 2.5 years following initial COVID-19 diagnosis.