We present a Gauss-Newton-Krylov solver for large deformation diffeomorphic image registration. We extend the publicly available CLAIRE library to multi-node multi-graphics processing unit (GPU) systems and introduce novel algorithmic modifications that significantly improve performance. Our contributions comprise; (i) a new preconditioner for the reduced-space Gauss-Newton Hessian system, (ii) a highly-optimized multi-node multi-GPU implementation exploiting device direct communication for the main computational kernels (interpolation, high-order finite difference operators and Fast-Fourier-Transform), and (iii) a comparison with state-of-the-art CPU and GPU implementations. We solve a 256^3-resolution image registration problem in five seconds on a single NVIDIA Tesla V100, with a performance speedup of 70% compared to the state-of-the-art. In our largest run, we register 2048^3 resolution images (25b unknowns; approximately 152x larger than the largest problem solved in state-of-the-art GPU implementations) on 64 nodes with 256 GPUs on TACC's Longhorn system.