An excimer in J-aggregates has been often considered as a self-trapped exciton originating from the free exciton excited on the same aggregate and relaxed through interaction with vibronic modes. Here we show that other types of excimers due to intermolecular off-diagonal interactions can be observed in J-aggregates of thiamonomethinecyanine dyes. These excimers arise owing to free excitons too, but they possess a longer formation time of more than 100 ps, indicating migration of free excitons to the excimer formation site, where they interact with a guest species in the ground state. Formation of the excimers occurs in solutions as a power law of concentration with an exponent of 1.5, showing that an excited aggregate should be twice longer than a ground-state guest species, consistent with the exciton coherence length of four molecules versus one dimer, respectively. Unlike the self-trapped exciton, lower temperatures lead to significant suppression of the observed excimer emission.