The paper addresses a new approach to supporting the continuous integration of modules for distributed applied software packages (scientific applications) that are developed in the Orlando Tools framework. We consider the packages for implementing experiments in heterogeneous distributed computing environments that integrate Grid systems, cloud platforms, and resources of public access supercomputer centers. Such packages are characterized by the modular structure, intense change of algorithmic knowledge implemented by modules, computations scalability, and execution in heterogeneous resources. In the packages, computational processes are represented by problem-solving schemes that closely correlate with the workflow concept. The essence and novelty of the proposed approach come from the merge of a methodology creating the packages with the modern practice of software development based on continuous integration. We automate and unify module assembly processes on both the dedicated servers and package developer machines through using the specialized virtual machines. In contrast to the well-known tools, we support the synthesis of the test problem-solving schemes in the automated mode. The practical applications of the developed prototype of the continuous integration system show the significant reducing the time of debugging, testing, and deploying the package modules.