Effort can be perceived both cognitively and physically, but the computational mechanisms underlying the motivation to invest effort in each domain remain unclear. In particular, it is unknown whether intensive physical training is associated with higher motivation specific to that domain, or whether it is accompanied by corresponding changes in cognitive motivation. Here, we tested a group of elite Oxford University rowers, and compared their behaviour to matched non-athletic controls. We trained participants on two tasks involving cognitive or physical effort. They then decided between a baseline low level of effort for low reward, versus higher levels of effort for higher rewards. Separate choices were made for the cognitive and physical tasks, which allowed us to computationally model motivation in each domain independently. As expected, athletes were willing to exert greater amounts of physical effort than non-athletes. Critically, however, the nature of cognitive effort-based decisions was different between groups, with a concave pattern of effort discounting for athletes but a convex pattern for non-athletes. These data suggest that the greater physical drive in athletes is accompanied by fundamentally different patterns of cognitive effort discounting, and suggests a complex relationship between motivation in the two domains.