Hybrid cloud is an integrated cloud computing environment utilizing a mix of public cloud, private cloud, and on-premise IT infrastructures. Workload awareness, defined as a detailed full range understanding of each individual workload, is essential in implementing the hybrid cloud. While it is critical to perform an accurate analysis to determine which workloads are appropriate for on-premise deployment versus which workloads can be migrated to a cloud off-premise, the assessment is mainly performed by rule or policy based approaches. In this paper, we introduce StackInsights, a novel cognitive system to automatically analyze and predict the cloud readiness of workloads for an enterprise. Our system harnesses the critical metrics across the entire stack: (1) infrastructure metrics, (2) data relevance metrics, and (3) application taxonomy, to identify workloads that have characteristics of (a) low sensitivity with respect to business security, criticality and compliance, and (b) low response time requirements and access patterns. Since the capture of the data relevance metrics involves an intrusive and in-depth scanning of the content of storage objects, a machine learning model is applied to perform the business relevance classification by learning from the meta level metrics harnessed across stack. In contrast to traditional methods, StackInsights significantly reduces the total time for hybrid cloud readiness assessment by orders of magnitude.