Cyber Physical Trust Systems (CPTS) are Cyber Physical Systems and Internet of Things enriched with trust as an explicit, measurable, testable and verifiable system component. In this paper, we propose to use blockchain, a distributed ledger technology, as the trust enabling system component for CPTS. We propose two schemes for CPTSs driven by blockchain in relation to two typical network model cases. We show that our proposed approach achieves the security properties, such as device identification, authentication, integrity, and non-repudiation, and provides protection against popular attacks, such as replay and spoofing. We provide formal proofs of those properties using the Tamarin Prover tool. We describe results of a proof-of-concept which implements a CPTS driven by blockchain for physical asset management and present a performance analysis of our implementation. We identify use cases in which CPTSs driven by blockchain find applications.