This letter analyzes the visual–inertial sensor fusion problem in the cooperative case of two agents, and proves that this sensor fusion problem is equivalent to a simple polynomial equations system that consists of several linear equations and three polynomial equations of second degree. The analytic solution of this polynomial equations system is easily obtained by using an algebraic method. In other words, this letter provides the analytic solution to the visual–inertial sensor fusion problem in the case of two agents. The power of the analytic solution is twofold. From one side, it allows us to determine the relative state between the agents (i.e., relative position, speed, and orientation) without the need of an initialization. From another side, it provides fundamental insights into all the theoretical aspects of the problem. This letter mainly focuses on the first issue. However, the analytic solution is also exploited to obtain basic structural properties of the problem that characterize the observability of the absolute scale and the relative orientation. Extensive simulations and real experiments show that the solution is successful in terms of precision and robustness.