Decentralized exchange markets leveraging blockchain have been proposed recently to provide open and equal access to traders, improve transparency and avoid single-point-of-compromise 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 order rate and account balance confidentiality 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 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.