The Coronavirus Disease 2019 (COVID-19) pandemic has broadly impacted university students’ customary life, resulting in remarkable levels of stress and psychological suffering. Although the acute phase of the crisis has been overcome, it does not imply that perceived stress related to the risk of contagion and to the changes in the relational life experienced over more than 1 year of the pandemic will promptly and abruptly decrease. This study aims at comparing university students’ psychological health conditions before and during the COVID-19 pandemic, but also at providing information on how psychological health conditions evolved over the 1 year of the pandemic. We analyzed data from a repeated cross-sectional survey on different samples of university students before the pandemic in 2017 (n = 545) and during the pandemic (n = 671). During the pandemic, data were collected at three stages (Stage 1, April 2020 n = 197; Stage 2, November 2020 n = 274; and Stage 3, April 2021 n = 200). The COVID-19 Student Stress Questionnaire (CSSQ) and the Symptom-Checklist-90-Revised (SCL-90-R) were used to assess, respectively, COVID-19-related stressors (Relationships and Academic Life, Isolation, and Fear of Contagion) and the presence of psychological symptoms. Psychological health conditions were compared at baseline and during the pandemic, whereas both psychological health conditions and perceived levels of COVID-19-related stressors were compared over the three pandemic stages. In addition, Logistic Regression was used to explore the associations between COVID-19-related stressors and psychological symptoms. Findings revealed a significant increase in symptoms of Depression (DEP), Phobic-Anxiety (PHOB), Obsessive-Compulsive (O-C), and Psychoticism (PSY) from pre to during the pandemic. Perceived levels of COVID-19-related stress and specific psychological symptoms significantly increased as the pandemic was progressing. COVID-19-related stressors emerged as significantly associated with several psychopathological symptoms. Findings are discussed with the aim of providing tailored interventions to prevent mental disease and promote psychological adjustment in this specific stage of transition within this exceptional global emergency.