Simple Summary: This study evaluates the occurrence of second primary neoplasms (SPNs) in individuals with a history of melanoma (MM) and identify factors that increase the risk in our population. A prospective cohort study was conducted, involving 529 MM survivors from January 2005 to August 2021. Among the 529 patients, 89 were diagnosed with SPNs, with 62 being skin tumors and 37 being solid organ tumors. The estimated probability of developing SPNs after MM diagnosis was found to increase over time, reaching 4.1% at 1 year, 11% at 5 years, and 19% at 10 years. Several factors were significantly associated with a higher risk of SPNs, including older age, primary MM location on the face or neck, and the histologic subtype of lentigo maligna MM. We conclude that individuals with primary MM located on the face and neck, as well as those with the histological subtype of lentigo maligna-MM, have a higher risk of developing SPNs. Age also independently influences the risk. Understanding these risk factors can assist in developing MM guidelines that provide specific follow-up recommendations for individuals at the highest risk. (1) Introduction: The association between melanoma (MM) and the occurrence of second primary neoplasms (SPNs) has been extensively studied, with reported incidence rates ranging from 1.5% to 20%. This study aims to evaluate the occurrence of SPNs in patients with a history of primary MM and to describe the factors that make the risk higher in our population. (2) Material and Methods: We conducted a prospective cohort study and calculated the incidence rates and relative risks (RR) for the development of different SPNs in 529 MM survivors from 1 January 2005 to 1 August 2021. Survival and mortality rates were obtained, and the Cox proportional hazards model was used to determine the demographic and MM-related factors that influence the overall risk. (3) Results: Among the 529 patients included, 89 were diagnosed with SPNs (29 prior to MM diagnosis, 11 synchronous, and 49 after MM), resulting in 62 skin tumors and 37 solid organ tumors. The estimated probability of developing SPNs after MM diagnosis was 4.1% at 1 year, 11% at 5 years, and 19% at 10 years. Older age, primary MM location on the face or neck, and histologic subtype of lentigo maligna mm were significantly associated with a higher risk of SPNs. (4) Conclusions: In our population, the risk of developing SPNs was higher in patients with primary MM located on the face and neck and with the histological subtype of lentigo maligna-MM. Age also independently influences the risk. Understanding these hazard factors can aid in the development of MM guidelines with specific follow-up recommendations for individuals with the highest risk.