The transition to college is a decisive stage for the acquisition of eating habits that continue into adulthood. The aim of this study is to assess the consumption of healthy elements of the Mediterranean diet in a group of university students and to evaluate whether the consumption pattern was related to sex, Body Mass Index (BMI), food addiction or the amount of physical activity performed. A total of 515 nursing students participated. The Mediterranean diet adherence questionnaire (PREDIMED), the food addiction scale (YFAS 2.0) and the International Physical Activity Questionnaire (IPAQ) were completed. For data analysis, multivariate analysis was performed with multiple linear regression and adjusted for sex, age, and BMI. The results showed that females consumed various types of meats (white/red, processed) in a healthier proportion (p < 0.05). Students that consumed more than one per day (unhealthy) of red/processed meats (mean difference (MD) = −0.49; 95% CI: −0.83; −0.15), soft drinks (MD = −0.82; 95% CI: 82–1.36; −0.27) and pastries (MD = −0.63; 95% CI: −0.97; −0.30) displayed higher food addiction scores. In addition, students who skipped breakfast also scored higher on food addiction (MD = 0.75; 95% CI: 0.31–1.19). Higher values of physical activity were observed in those who presented a healthy consumption of vegetables (MD = 140.86; 95% CI: 72.71–209.02), fruit (MD = 145.78; 95% CI: 69.35–222.21), legumes (MD = 136.46; 95% CI: 60.43–212.50) and nuts (MD = 74.36; 95% CI: 14.23–134.49). Students who consumed more red or processed meats, more pastries and more soft drinks had higher values of food addiction, while those who consumed more vegetables, fruits, legumes, and nuts had more minutes of physical activity per week. These findings invite us to insist on expanding knowledge regarding the health benefits of consuming a Mediterranean-type diet as a whole. The healthy consumption of fish, fruit and legumes should also be emphasized, especially among university students.