Recently, blockchain has gained momentum in the academic community thanks to its decentralization, immutability, transparency and security. As an emerging paradigm, Multiaccess Edge Computing (MEC) has been widely used to provide computation and storage resources to mobile user equipments (UE) at the edge of the network for improving the performance of mobile applications. In this paper, we propose a novel blockchain-based MEC architecture where UEs can offload their computation tasks to the MEC servers. In particular, a blockchain network is deployed and hosted on the MEC platform as Blockchain as a Service (BaaS) that supports smart contract-based resource trading and transaction mining services for mobile task offloading. To enhance the performance of the blockchain-empowered MEC system, we propose a joint scheme of computation offloading and blockchain mining. Accordingly, an optimization problem is formulated to maximize edge service revenue and blockchain mining reward while minimizing the service computation latency with respect to constraints of user service demands and hash power resource. We then propose a novel Deep Reinforcement Learning (DRL) approach using a double deep Q-network (DQN) algorithm to solve the proposed problem. Numerical results demonstrate that the proposed scheme outperforms the other baseline methods in terms of better system utility with computational efficiency. Experiment results also verify that the trading contract design is efficient with low operation cost, showing the feasibility of the proposed scheme.