Background and Methods: Vaccination is currently considered the most successful strategy for combating the SARS-CoV-2 virus. According to short-term clinical trials, protection against infection is estimated to reach up to 95% after complete vaccination (≥14 days after receipt of all recommended COVID-19 vaccine doses). Nevertheless, infections despite vaccination, so-called breakthrough infections, are documented. Even though they are more likely to have a milder or even asymptomatic course, the assessment of further transmission is highly relevant for successful containment. Therefore, we calculated the real-world transmission risk from fully vaccinated patients (vaccination group, VG) to their close contacts (CP) compared with the risk from unvaccinated reference persons matched according to age, sex, and virus type (control group = CG) utilizing data from Cologne’s health department. Results: A total of 357 breakthrough infections occurred among Cologne residents between 27 December 2020 (the date of the first vaccination in Cologne) and 6 August 2021. Of the 979 CPs in VG, 99 (10.1%) became infected. In CG, 303 of 802 CPs (37.8%) became infected. Factors promoting transmission included non-vaccinated status (β = 0.237; p < 0.001), male sex (β = 0.079; p = 0.049), the presence of symptoms (β = −0.125; p = 0.005), and lower cycle threshold value (β = −0.125; p = 0.032). This model explained 14.0% of the variance (corr. R²). Conclusion: The number of transmissions from unvaccinated controls was three times higher than from fully vaccinated patients. These real-world data underscore the importance of vaccination in enabling the relaxation of stringent and restrictive general pandemic control measures.