Context: Several secondary studies have investigated the relationship between internal quality attributes, source code metrics and external quality attributes. Sometimes they have contradictory results. Objective: We synthesize evidence of the link between internal quality attributes, source code metrics and external quality attributes along with the efficacy of the prediction models used. Method: We conducted a tertiary review to identify, evaluate and synthesize secondary studies. We used several characteristics of secondary studies as indicators for the strength of evidence and considered them when synthesizing the results. Results: From 711 secondary studies, we identified 15 secondary studies that have investigated the link between source code and external quality. Our results show : (1) primarily, the focus has been on object-oriented systems, (2) maintainability and reliability are most often linked to internal quality attributes and source code metrics, with only one secondary study reporting evidence for security, (3) only a small set of complexity, coupling, and size-related source code metrics report a consistent positive link with maintainability and reliability, and (4) group method of data handling (GMDH) based prediction models have performed better than other prediction models for maintainability prediction. Conclusions: Based on our results, lines of code, coupling, complexity and the cohesion metrics from Chidamber & Kemerer (CK) metrics are good indicators of maintainability with consistent evidence from high and moderate-quality secondary studies. Similarly, four CK metrics related to coupling, complexity and cohesion are good indicators of reliability, while inheritance and certain cohesion metrics show no consistent evidence of links to maintainability and reliability. Further empirical studies are needed to explore the link between internal quality attributes, source code metrics and other external quality attributes, including functionality, portability, and usability. The results will help researchers and practitioners understand the body of knowledge on the subject and identify future research directions. © 2023 The Author(s)