Tennis coaches display significant influence, catalyzing changes in athlete performance, motivation, and overall well-being. Research on coaches’ motivations and their impact on coaching style, work, and well-being is limited, especially in individual sports like tennis. Based on self-determination (SDT) and achievement goal (AGT) theories, the aim of the present study was to examine the relationships of coaches’ self-determined motivation (intrinsic, extrinsic, and amotivation), basic psychological needs satisfaction (autonomy, relatedness, and competence), and achievement goals (self-improvement—SI, self-enhancement—SE, self-transcendence—ST) with their coach-created empowering-disempowering motivational climate, work engagement, and well-being (subjective vitality). Participants were 106 tennis coaches from Greece (66 males and 40 females), with an average age of 41.30 ± 12.54 years and coaching experience ranging from six months to 40 years. Data was collected through online questionnaires. Correlation analysis revealed that intrinsic and extrinsic motivation, satisfaction of the three basic psychological needs, and achievement goals were found to be positively related to an empowering climate, work engagement, and subjective vitality. Coaches’ amotivation was positively related to a disempowering climate. Multiple regression analyses showed that autonomy and ST achievement goals significantly predicted tennis coaches’ empowering motivational climate, while none of the independent variables were significant predictors of the disempowering motivational climate. Additionally, intrinsic motivation and ST goal significantly predicted tennis coaches’ work engagement, while autonomy and ST goal significantly predicted their subjective vitality. It is advisable for forthcoming coach education initiatives to consider these findings as an additional justification for tennis coaches to incorporate multiple perspectives into their coaching methodologies.