Summary: Despite the apparent need to study reversible reactions between molecules confined to a two-dimensional space such as the cell membrane, exact Green functions for this case have not been reported. Here, we present exact analytical Green functions for a Brownian particle reversibly reacting with a fixed reaction center in a finite two-dimensional circular region with reflecting or absorbing boundaries, considering either a spherically symmetric initial distribution or a particle that is initially bound. We show that Green’s function can be used to predict the effect of measurement uncertainties on the outcome of single-particle/molecule-tracking experiments in which molecular interactions are investigated. Hence, we bridge the gap between previously known solutions in one dimension [N. Agmon, “Diffusion with back reaction”, J. Chem. Phys. 81, No. 6, 2811–2817 (1984; doi:10.1063/1.447954)] and three dimensions H. Kim and K. J. Shin, “Exact solution of the reversible diffusion-influenced reaction for an isolated pair in three dimensions”, Phys. Rev. Lett. 82, No. 7, 1578–1581 (1999; doi:10.1103/PhysRevLett.82.1578)], and provide an example of how the knowledge of Green’s function can be used to predict experimentally accessible quantities.