For decades, software engineering research and practice has focused primarily on technological and process-related factors. Today, there is a growing interest in organizational, social, and psychological factors, including well-being. Organizational studies show that well-being contributes to work outcomes, including creativity, performance, and productivity. But despite its importance, the predictors and outcomes of software engineers' well-being as a multidimensional construct to date are under-researched. This paper reports on the multidimensional well-being of professional software engineers and generates insights for the future research in this area. 44 quantitative survey studies published between 2000 and 2023 were selected and synthesized both quantitatively and qualitatively through a systematic literature review. The results of the review were further analyzed to construct a quantitatively-testable theory, detailing the predictors and outcomes of well-being in software engineering organizations. The total number of research participants included in the selected studies is 16,086 software engineering professionals from at least 42 countries. The literature review identified various measures, constructs, and indicators of well-being, as well as its predictors and outcomes. The theory, based on cumulative results of carefully selected quantitative studies, is an attempt to "correct the record" by establishing well-being in software engineering as a meta-construct of hedonic, eudaimonic, and integrated or hedaimonic qualities predicted by different individual, team and organizational factors and impacting the functioning of software engineers and their organizations. The review highlighted the under-researched aspects of well-being in software engineering and confirmed the need for more advanced quantitative studies. We hope that the theory will benefit researchers in conducting future studies and practitioners in developing nuanced and science-based interventions for improving software engineers' well-being.