The internet of medical things (IoMT) is a smart medical device structure that includes apps, health services, and systems. These medical equipment and applications are linked to healthcare systems via the internet. Because IoT devices lack computational power, the collected data can be processed and analyzed in the cloud by more computationally intensive tools. Cloud computing in IoMT is also used to store IoT data as part of a collaborative effort. Cloud computing has provided new avenues for providing services to users with better user experience, scalability, and proper resource utilization compared to traditional platforms. However, these cloud platforms are susceptible to several security breaches evident from recent and past incidents. Trust management is a crucial feature required for providing secure and reliable service to users. The traditional trust management protocols in the cloud computing situation are centralized and result in single-point failure. Blockchain has emerged as the possible use case for the domain that requires trust and reliability in several aspects. Different researchers have presented various blockchain-based trust management approaches. This study reviews the trust challenges in cloud computing and analyzes how blockchain technology addresses these challenges using blockchain-based trust management frameworks. There are ten (10) solutions under two broad categories of decentralization and security. These challenges are centralization, huge overhead, trust evidence, less adaptive, and inaccuracy. This systematic review has been performed in six stages: identifying the research question, research methods, screening the related articles, abstract and keyword examination, data retrieval, and mapping processing. Atlas.ti software is used to analyze the relevant articles based on keywords. A total of 70 codes and 262 quotations are compiled, and furthermore, these quotations are categorized using manual coding. Finally, 20 solutions under two main categories of decentralization and security were retrieved. Out of these ten (10) solutions, three (03) fell in the security category, and the rest seven (07) came under the decentralization category.