The COVID-19 pandemic has profoundly impacted on cancer patients’ psychological well-being and clinical status. We assessed the levels of anxiety, depression, and distress and the attitude towards COVID-19 vaccination in cancer patients, accepting vaccination at the Verona University Hospital and Camposampiero Hospital in the Veneto region. Self-reported questionnaires were administered to patients undergoing COVID-19 vaccination between March and May 2021 (first and second dose). Twenty-seven items were investigated: i) demographics/clinical characteristics; ii) anxiety, depression, and distress (Hospital Anxiety and Depression Scale—HADS—and Distress Thermometer—DT); iii) four specific items regarding awareness about infection risks, interference with anticancer treatments, and vaccine side effects. Sixty-two and 57% of the patients who accepted to be vaccinated responded to the survey in the two participating Hospitals, respectively. Mean age was 63 years (SD: 12 years; range 19–94 years), women were slightly more prevalent (57.6%), most participants were married (70%), and either worker or retired (60%). Borderline and clinical levels of anxiety were recorded in 14% and 10% of respondents; borderline and clinical levels of depression in 14% and 8%; and moderate and severe distress levels in 33% and 9%. Overall, there was high confidence that vaccination would reduce the risk of contracting COVID-19 (70%), which would make patients feel less worried about contracting the infection (60%). Fear that vaccine-related side effects would interfere with anticancer treatment and/or global health status was low (10% and 9% for items 3 and 4, respectively) and significantly associated with baseline levels of anxiety, depression, and distress at multivariate analysis. Results did not differ between the Verona and Camposampiero cohorts. During the COVID-19 vaccination campaign, adult cancer patients demonstrated high levels of confidence towards vaccination; baseline levels of anxiety, depression, and distress were the only significant predictors of reduced confidence.