We use a sample of newly-discovered globular clusters from the Pan-Andromeda Archaeological Survey (PAndAS) in combination with previously-catalogued objects to map the spatial distribution of globular clusters in the M31 halo. At projected radii beyond ~30 kpc, where large coherent stellar streams are readily distinguished in the field, there is a striking correlation between these features and the positions of the globular clusters. Adopting a simple Monte Carlo approach, we test the significance of this association by computing the probability that it could be due to the chance alignment of globular clusters smoothly distributed in the M31 halo. We find the likelihood of this possibility is low, below 1%, and conclude that the observed spatial coincidence between globular clusters and multiple tidal debris streams in the outer halo of M31 reflects a genuine physical association. Our results imply that the majority of the remote globular cluster system of M31 has been assembled as a consequence of the accretion of cluster-bearing satellite galaxies. This constitutes the most direct evidence to date that the outer halo globular cluster populations in some galaxies are largely accreted.