The increasing complexity of reactive systems can be mitigated with the use of components and composition languages in model-driven engineering. Designing composition languages is a challenge itself as both practical applicability (support for different composition approaches in various application domains), and precise formal semantics (support for verification and code generation) have to be taken into account. In our Gamma Statechart Composition Framework, we designed and implemented a composition language for the synchronous, cascade synchronous, and asynchronous composition of statechart-based reactive components. We formalized the semantics of this composition language that provides the basis for generating composition-related Java source code as well as mapping the composite system to a back-end model checker for formal verification and model-based test case generation. In this paper, we present the composition language with its formal semantics, putting special emphasis on design decisions related to the language and their effects on verifiability and applicability. Furthermore, we demonstrate the design and verification functionality of the composition framework by presenting case studies from the cyber-physical system domain.