Childhood vaccination remains a cornerstone of public health, yet in Ghana, significant disparities persist, particularly in rural and low-income settings. This study addresses a critical gap by applying logistic regression modeling to population-based data from 2020 to 2024, aiming to identify the determinants influencing full vaccination uptake among children aged 12-23 months. Using a sample of 1,000 respondents extracted from the Ghana Demographic and Health Survey and supplemented by Ghana Health Service and UNICEF data, the research employed binary logistic regression, chi-square, ANOVA, and Pearson correlation analyses to examine variables such as maternal education, household wealth, and health service accessibility. The findings revealed that maternal education (OR = 2.10, p < 0.001), household wealth (OR = 1.85, p < 0.001), proximity to clinics (OR = 0.70, p = 0.002), and antenatal care visits (OR = 2.35, p < 0.001) were significant predictors of full vaccination. A strong inverse correlation was observed between distance to clinics and vaccination uptake (r = -0.72, p < 0.001), while the overall model showed excellent fit (Nagelkerke R² = 0.48; Hosmer-Lemeshow p = 0.57). The interaction of high maternal education and wealth yielded a 91.2% predicted probability of full vaccination, compared to just 54.7% among children with neither. These results imply that tailored interventions focusing on education, economic support, and healthcare access can substantially enhance immunization coverage. The study recommends integrated strategies, including conditional cash transfers, mobile clinics, and female literacy programs, to bridge existing gaps and meet the WHO’s 95% vaccination target.