We present a two-way coupled fluid–structure interaction scheme for rigid bodies using a two-population lattice Boltzmann formulation for compressible flows. An arbitrary Lagrangian–Eulerian formulation of the discrete Boltzmann equation on body-fitted meshes is used in combination with polynomial blending functions. The blending function approach localizes mesh deformation and allows treating multiple moving bodies with a minimal computational overhead. We validate the model with several test cases of vortex induced vibrations of single and tandem cylinders and show that it can accurately describe dynamic behavior of these systems. Finally, in the compressible regime, we demonstrate that the proposed model accurately captures complex phenomena such as transonic flutter over an airfoil.