The aim of the presented study was to verify the relationship between the level of work engagement and organizational commitment and work satisfaction experienced by employees, taking into account intermediary variables—i.e. the climate at the organization and the phenomenon of silence in the organization. The survey involved a total of 131 employees of the National Revenue Administration, including 35 males and 96 females. Five methods were used to verify the questions and research hypotheses: Allen and Meyer’s Organizational Commitment Scale, the AVEM questionnaire, Paluchowski’s Organizational Climate Questionnaire, the four forms of the Organizational Silence Scale, and the Job Descriptive Index (JDI). The results of the research show that there is a significant relationship between work engagement and organizational commitment and work satisfaction.