Decentralized exchange markets leveraging blockchain have been proposed recently to provide open and equal access to traders, improve transparency and reduce systemic risk of centralized exchanges. However, they compromise on the privacy of traders with respect to their asset ownership, account balance, order details and their identity. In this paper, we present Rialto, a fully decentralized privacy-preserving exchange marketplace with support for matching trade orders, on-chain settlement and market price discovery. Rialto provides confidentiality of order rates and account balances and unlinkability between traders and their trade orders, while retaining the desirable properties of a traditional marketplace like front-running resilience and market fairness. We define formal security notions and present a security analysis of the marketplace. We perform a detailed evaluation of our solution, demonstrate that it scales well and is suitable for a large class of goods and financial instruments traded in modern exchange markets.