A sharp-interface model employing the extended finite element method is presented. It is designed to capture the prominent γ-γ′ phase transformation in nickel-based superalloys. The novel combination of crystal plasticity and sharp-interface theory outlines a good modeling alternative to approaches based on the Cahn–Hilliard equation. The transformation is driven by diffusion of solute γ′-forming elements in the γ-phase. Boundary conditions for the diffusion problem are computed by the stress-modified Gibbs–Thomson equation. The normal mass balance of solute atoms at the interface yields the normal interface velocity, which is integrated in time by a level set procedure. In order to capture the influence of dislocation glide and climb on interface motion, a crystal plasticity model is assumed to describe the constitutive behaviour of the γ-phase. Cuboidal equilibrium shapes and Ostwald ripening can be reproduced. According to the model, in low γ′ volume-fraction alloys with separated γ′-precipitates, interface movement does not have a significant effect on tensile creep behaviour at various lattice orientations.