This paper presents SigVM, the first blockchain virtual machine that extends EVM to support an event-driven execution model, enabling developers to build truly decentralized smart contracts. Contracts in SigVM can emit signal events, on which other contracts can listen. Once an event is triggered, corresponding handler functions are automatically executed as signal transactions. We build an end-to-end blockchain platform SigChain and a contract language compiler SigSolid to realize the potential of SigVM. Experimental results show that our benchmark applications can be reimplemented with SigVM in a truly decentralized way, eliminating the dependency on centralized and unreliable mechanisms like off-chain relay servers. The development effort of reimplementing these contracts with SigVM is small, i.e., we modified on average $3.17%$ of the contract code. The runtime and the gas overhead of SigVM on these contracts is negligible.