The emergence of new technologies, artificial Intelligence, BANI environment and multidimensional complexity in projects requires project managers to have an innovative instinct to formulate efficient project management practices to achieve project success. Most articles in the extant literature have discussed leadership factors impacting project success; however, leadership behavioural practices encompassing characteristics/dimensions have not been considered and discussed in a unified manner. Therefore, a need arises with an objective for such a study to bridge the gap of a systematic literature review on leadership behavioural practice characteristics and provide a unified summarised effort to understand relationships with project success from relevant studies between 2000 and 2021. A sample of 72 out of 2805 articles was finally selected for rigorous analysis in a seven-step literature review process. This SLR has identified high to moderate levels of tangible managerial interpersonal and emotional behavioural practice characteristics compared to low-level task-oriented and intellectual practices on construction projects. Compelling evidence shows that relationship-building and people-oriented project leaders using effective communication and collaborative working are highly valued compared to task-oriented project leaders on successful construction projects. Effective leadership practices and findings from this SLR will provide a benchmark for future researchers to investigate further construction projects to generalize SLR outcomes on a broader scale. In addition, project organizations can use our identified cluster listings of behavioural practice characteristics during their recruitment process of project professionals. Low-valued soft skills in our analysis need more investigations in future research.