The distributed observer is effective for solving the leader-following attitude consensus problem of multiple rigid-body systems. In this paper, we first develop an event-triggered distributed observer for a leader rigid body system over jointly connected switching networks. It is shown that, under two standard assumptions, the state of the event-triggered distributed observer will exponentially converge to the leader’s state and the inter-event time sequence admits a positive lower bound. Then, we synthesize an event-triggered distributed observer-based control law to solve the leader following attitude consensus problem of multiple rigid body systems. The effectiveness of our design will be illustrated with a numerical example.