Cognitive disorders remain a major cause of disability in Multiple Sclerosis (MS). They lead to unemployment, the need for daily assistance, and a poor quality of life. The understanding of the origin, factors, processes, and consequences of cognitive disfunction is key to its prevention, early diagnosis, and rehabilitation. The neuropsychological testing and continuous monitoring of cognitive status as part of the overall evaluation of patients with MS in parallel with clinical and paraclinical examinations are highly recommended. In order to improve health and disease understanding, a close linkage between fundamental, clinical, epidemiological, and socio-economic research is required. The effective sharing of data, standardized data processing, and the linkage of such data with large-scale cohort studies is a prerequisite for the translation of research findings into the clinical setting. In this context, this paper proposes a software platform for the cognitive assessment and rehabilitation of patients with MS called CogniSoft. The platform automates the Beck Depression Inventory (BDI-II) test and diagnostic tests for the evaluation of memory and executive functions based on the nature of Brief International Cognitive Assessment for MS (BICAMS), as well as implementing a set of games for cognitive rehabilitation based on BICAMS. The software architecture, core modules, and technologies used for their implementation are presented. Special attention is given to the development of cognitive tests for diagnostics and rehabilitation. Their automation enables better perception, avoids bias as a result of conducting the classic paper tests of various neurophysiologists, provides easy administration, and allows data collection in a uniform manner, which further enables analysis using statistical and machine learning algorithms. The CogniSoft platform is registered as medical software by the Bulgarian Drug Agency and it is currently deployed in the Neurological Clinic of the National Hospital of Cardiology in Sofia, Bulgaria. The first experiments prove the feasibility of the platform, showing that it saves time and financial resources while providing subjectivity in the interpretation of the cognitive test results.