Self-determination theory (SDT) postulates that all humans have basic psychological needs for autonomy, competence, and relatedness as they provide the necessary nutrients for psychological growth and wellness. However, the long-standing theoretical claims regarding the necessity of basic psychological needs satisfaction for well-being have received comparably less empirical attention, due in part to a theory-method misalignment. Regression techniques imply an additive sufficiency logic and are unsuitable for testing necessity statements in SDT. To solve the theory-method mismatch, we employ necessary condition analysis (NCA) to examine the necessary roles of basic psychological needs satisfaction for employee evaluative well-being (job satisfaction), hedonic well-being (positive affect), and eudaimonic well-being (work engagement, thriving at work, and work meaningfulness). A two-wave field study conducted in the U.S. supports that each basic psychological need is necessary for all five employee well-being indicators (N = 376; Study 1). We replicated these findings among 373 U.K. employees (Study 2) and 345 Chinese employees (Study 3). We also found that power and status are generally not necessary for well-being (Study 2). Overall, these findings highlight the necessity of satisfying employees’ basic psychological needs for autonomy, competence, and relatedness in management practices.