This study is based on frameworks of the eudaimonic activity model and the basic psychological needs theory, with two purposes: one, to prove the validity of a translation and adaptation of the Basic Psychological Needs Satisfaction and Frustration Scale; two, to analyze how the basic psychological satisfaction and frustration needs influences the well-being of university physical activity and sports students, through sex. A total of 830 University students of physical activity and sports with an age between 17 and 31 years (M = 20.70 years; ±2.96) participated. The sample was divided into two subsamples by random selection of 50% of the cases, preserving the relative distribution of sex and age. The first subsample was used to validate the adaptation of the Basic Psychological Need Satisfaction and Frustration Scale to Spanish as spoken in Mexico (Study 1); and the second subsample was used to test a proposed sequential theoretical model (Study 2). In Study 1, the CFA supported the structure of six factors—satisfaction of needs for autonomy, relatedness and competence; frustration of needs for autonomy, relatedness and competence (RMSR = 0.04; RMSEA = 0.046; TLI = 0.93; CFI = 0.94)—as well as the structure of six first-order factors plus two second-order factors—psychological need satisfaction and psychological need frustration (RMSR = 0.05; RMSEA = 0.055; TLI; CFI = 0.91). Both structures were equivalent between men and women. In Study 2, the results of the structural equations model show good fit (RMSEA = 0.05; TLI = 0.90; CFI = 0.92), indicating that the needs satisfied and frustrated contribute in a unique way to indicators of eudaimonic well-being (i.e., subjective vitality) and subjective well-being (i.e., life satisfaction), being equivalent through sex. In conclusion, satisfaction of competence, relationships and autonomy are essential nutrients for a positive performance in this sample.