In recent decades, a number of studies have examined whether various non-human animals understand their partner’s role in cooperative situations. Yet the relatively tolerant timing requirements of these tasks make it theoretically possible for animals to succeed by using simple behavioural strategies rather than by jointly intended coordination. Here we investigated whether bottlenose dolphins could understand a cooperative partner’s role by testing whether they could learn a button-pressing task requiring precise behavioural synchronisation. Specifically, members of cooperative dyads were required to swim across a lagoon and each press their own underwater button simultaneously (within a 1-second time window), whether sent together or with a delay between partners of 1-20 seconds. We found that dolphins were able to work together with extreme precision even when they had to wait for their partner, and that their coordination improved over the course of the study, with the time between button presses in the latter trials averaging 370 milliseconds. These findings show that bottlenose dolphins can learn to understand their partner’s role in a cooperative situation, and suggest that the behavioural synchronisation evident in wild dolphins’ synchronous movement and coordinated alliance displays may be a generalized cognitive ability that can also be used to solve novel cooperative tasks.