We provide universally-optimal distributed graph algorithms for (1+ε)-approximate shortest path problems including shortest-path-tree and transshipment.The universal optimality of our algorithms guarantees that, on any n-node network G, our algorithm completes in T •n o(1) rounds whenever a T -round algorithm exists for G. This includes D • n o(1) -round algorithms for any planar or excluded-minor network. Our algorithms never require more than ( √ n + D) • n o(1) rounds, resulting in the first sub-linear-round distributed algorithm for transshipment.