Engineering programmes face a dual challenge: high student stress and an industry demand for graduates with robust leadership skills. Although well-being is known to foster leadership in the workplace, its multidimensional links to leadership development within undergraduate engineering remain underexplored. This study investigates how Gallup's five well-being domains: Career/Purpose, Social, Financial, Physical, and Community relate to leadership readiness and whether these relationships differ across degree tracks. Thirtyfive well-being indicators were collected from 365 Mexican students in Computer Science and Technology (214), Biomedical (98), and Innovation and Development Engineering (53). Spearman correlations assessed domain-leadership associations; Kruskal-Wallis tests compared domain scores across programmes. Leadership readiness aligned most strongly with Career/Purpose well-being and showed large-effect correlations with Community and Physical domains; SocialRomantic ties were minor. Programme contrasts revealed significant gaps in Physical, Career, and Community well-being, while Social and Financial scores were uniform. Comparisons between programs showed big differences in Physical, Career, and Community well-being, while Social and Financial scores were the same. Consequently, professional purpose, civic engagement, and health perceptions are more significantly influenced by the curricular context than by economic or interpersonal factors. Targeted interventions, such as wellness modules for sedentary IT groups, career-planning workshops for Biomedical students, and community-embedded projects for Innovation and Development engineers, can help people become better leaders. The findings suggest that programme context, rather than interpersonal or economic factors, drives betweenprogramme differences.