This paper addresses the problem of reaching consensus among a group of agents that evolve in continuous-time and exchange information at discrete-time instants, referred to as update times. Each agent has its own sequence of update times and therefore the agents are not required to keep synchronized clocks among them. At each update time, an agent receives from a subset of the other agents their state, as determined by the communication topology that may be time-varying. Due to transmission delays, the information may be received by an agent with latency. In our proposed solution, the state of each agent is augmented with an extra state variable that is updated instantaneously at update times. Between updates, the original state and the extra variable both evolve in a continuous fashion. It is shown that consensus is reached asymptotically by reducing the original problem involving continuous-time variables and asynchronous communications to a discrete-time equivalent and using known results for discrete-time consensus.