Modern big data computing systems exemplified by Hadoop employ parallel processing based on distributed storage. The results produced by parallel tasks such as computing modules in scientific workflows or reducers in the MapReduce framework are typically stored in a distributed file system across multiple data nodes. However, most existing systems do not provide a mechanism to compose such distributed information, as required by many big data applications. We construct analytical cost models and formulate a Distributed Information Composition problem in Big Data Systems, referred to as DIC-BDS, to aggregate multiple datasets stored as data blocks in Hadoop Distributed File System (HDFS) using a composition operator of specific complexity to produce one final output. We rigorously prove that DIC-BDS is NP-complete, and propose two heuristic algorithms: Fixed-window Distributed Composition Scheme (FDCS) and Dynamic-window Distributed Composition Scheme with Delay (DDCS-D). We conduct extensive experiments in Google clouds with various composition operators of commonly considered degrees of complexity including O(n), O(n log n), and O(n2). Experimental results illustrate the performance superiority of the proposed solutions over existing methods. Specifically, FDCS outperforms all other algorithms in comparison with a composition operator of complexity O(n) or O(n log n), while DDCS-D achieves the minimum total composition time with a composition operator of complexity O(n2). These algorithms provide an additional level of data processing for efficient information aggregation in existing workflow and big data systems.