  We prove the following rigidity results. Coarse equivalences between
Euclidean buildings preserve spherical buildings at infinity. If all
irreducible factors have dimension at least two, then coarsely equivalent
Euclidean buildings are isometric (up to scaling factors). If in addition none
of the irreducible factors is a Euclidean cone, then the isometry is unique and
has finite distance from the coarse equivalence.
