In this work, we propose a PRivAcy-Diversity-Aware Team Formation framework, namely PRADA-TF, that can be deployed based on the trust relationships between users in online social networks (OSNs). Our proposed PRADA-TF is mainly designed to reflect team members' domain expertise and privacy preserving preferences when a task requires a wide range of diverse domain expertise for its successful completion. The proposed PRADA-TF aims to form a team for maximizing its productivity based on members' characteristics in their diversity, privacy preserving, and information sharing. We leveraged a game theory called Mechanism Design in order for a mechanism designer as a team leader to select team members that can maximize the team's social welfare, which is the sum of all team members' utilities considering team productivity, members' privacy preserving, and potential privacy loss caused by information sharing. To screen a set of candidate teams in the OSN, we built an expert social network based on real co-authorship datasets (i.e., Netscience) with 1,590 scientists, used the semi-synthetic datasets to construct a trust network based on a belief model called Subjective Logic, and identified trustworthy users as candidate team members. Via our extensive simulation experiments, we compared the seven different TF schemes, including our proposed and existing TF algorithms, and analyzed the key factors that can significantly impact the expected and actual social welfare, expected and actual potential privacy leakout, and team diversity of a selected team.