•We propose a governance structure for mandatory data sharing on data-driven markets.•A governance structure details investigation, decision making, and enforcement.•Optimal governance combines economically efficient centralization with legally necessary decentralization.•We show how and why it differs from current EU legal initiatives (DMA, DSA). To prevent market tipping, which inhibits innovation, there is an urgent need to mandate sharing of user information in data-driven markets. Existing legal mechanisms to impose data sharing under EU competition law and data portability under the GDPR are not sufficient to tackle this problem. Mandated data sharing requires the design of a governance structure that combines elements of economically efficient centralization with legally necessary decentralization. We identify three feasible options. One is to centralize investigations and enforcement in a European Data Sharing Agency (EDSA), while decision-making power lies with National Competition Authorities in a Board of Supervisors. The second option is to set up a Data Sharing Cooperation Network coordinated through a European Data Sharing Board, with the National Competition Authority best placed to run the investigation adjudicating and enforcing the mandatory data-sharing decision across the EU. A third option is to mix both governance structures and to task national authorities to investigate and adjudicate and the EU-level EDSA with enforcement of data sharing.