May owns the Marshall Field's and Lord and Taylor Chains, while Federated operates Macy's and Bloomingdale's. Together, they'll create a company with 1,000 stores and $30 billion in annual sales.
Federated's purchase of May will extend Federated's 34-state retail operation into a total of 49 states, along with Guam, Puerto Rico and the District of Columbia.
The merger comes as retailers are looking to consolidate to reduce advertising and other costs while gaining bargaining power with suppliers.
Last November, K-Mart Holding Corporation agreed to buy Sears, Roebuck and Company for $11.5 billion.