Background: Immunization against SARS-CoV-2 is essential for vulnerable solid organ transplant (SOT) recipients who are at risk of infection. However, there are concerns about suboptimal immunogenicity, especially in humoral immunity (HMI), and limited exploration of cell-mediated immune (CMI) responses. The primary objective of this study was to assess the immunogenicity of ChAdOx1 nCoV-19 vaccination in SOT recipients. The secondary endpoint was to evaluate factors that affect immunogenicity and adverse events (AEs) following immunization in SOT recipients. Methods: All adult SOT recipients who received the two-dose ChAdOx1 nCoV-19 vaccine at a 12-week interval underwent measurements of HMI by evaluating anti-receptor-binding domain (RBD) IgG levels and CMI by investigating SARS-CoV-2-specific T cell and B cell responses before and after complete vaccination, around 2–4 weeks post-vaccination, and compared to controls. AEs were monitored in all participants. Results: The study included 63 SOT recipients: 44 kidney recipients, 16 liver recipients, and 3 heart transplant recipients, along with 11 immunocompetent controls. Among SOT recipients, 36% were female, and the median (IQR) age was 52 (42–61). The median (IQR) time since transplant was 55 (28–123) months. After the second dose, the median (IQR) anti-RBD antibody levels were significantly lower in SOT recipients compared to those in the control group (8.3 [0.4–46.0] vs. 272.2 [178.1–551.6] BAU/mL, p < 0.01). This resulted in a seroconversion rate (anti-RBD antibody > 7.1 BAU/mL) of 51% among SOT recipients and 100% among controls (p = 0.008). Receiving the vaccine beyond one year post-transplant significantly affected seroconversion (OR 9.04, 95% CI 1.04–78.56, p = 0.046), and low-dose mycophenolic acid marginally affected seroconversion (OR 2.67, 95% CI 0.89–7.96, p = 0.079). RBD-specific B cell responses were also significantly lower compared to those in the control group (0 [0–4] vs. 10 [6–22] SFUs/106 PBMCs, p = 0.001). Similarly, S1- and SNMO-specific T cell responses were significantly lower compared to those in the control group (48 [16–128] vs. 216 [132–356] SFUs/106 PBMCs, p = 0.004 and 20 [4–48] vs. 92 [72–320] SFUs/106 PBMCs, p = 0.004). AEs were generally mild and spontaneously resolved. Conclusions: SOT recipients who received the full two-dose ChAdOx1 nCoV-19 vaccine demonstrated significantly diminished HMI and CMI responses compared to immunocompetent individuals. Consideration should be given to administering additional vaccine doses or optimizing immunosuppressant regimens during vaccination (Thai Clinical Trial Registry: TCTR20210523002).