Context: Research has shown that a significant number of software projects fail due to social issues such as team or personality conflicts. However, only a limited number of empirical studies have been undertaken to understand the impact of individuals' personalities on software team configurations. These studies suffer from an important limitation as they lack a systematic and rigorous method to relate personality traits of software practitioners and software team structures. Objective: Based on an interactive personality profiling approach, the goal of this study is to reveal the personality traits of software practitioners with an aim to explore effective software team structures. Method: To explore the importance of individuals' personalities on software teams, we employed a two-step empirical approach. Firstly, to assess the personality traits of software practitioners, we developed a context-specific survey instrument, which was conducted on 216 participants from a middle-sized software company. Secondly, we propose a novel team personality illustration method to visualize team structures. Results: Study results indicated that effective team structures support teams with higher emotional stability, agreeableness, extroversion, and conscientiousness personality traits. Conclusion: Furthermore, empirical results of the current study show that extroversion trait was more predominant than previously suggested in the literature, which was especially more observable among agile software development teams.