Theories of evolution of dispersal study how organisms living in heterogeneous landscapes should move to maximize their fitness. An evolutionarily stable strategy (ESS) is a movement strategy that cannot be invaded by any other strategy. Classical reaction-diffusion models assume that landscape quality varies continuously. Landscape ecologists consider landscapes as mosaics of patches where individuals can make movement decisions at sharp interfaces between patches of different quality. We use a recent formulation of reaction-diffusion systems in patchy landscapes to study the evolution of dispersal strategies via adaptive dynamics. Two independent analytical approaches allow us to explicitly calculate the optimal strategy. This ESS turns out to be the one that leads to the ideal-free distribution.