Surface brightness profiles for 23 M31 star clusters were measured using images from the Wide Field Planetary Camera 2 on the Hubble Space Telescope, and fitted to two types of models to determine the clusters' structural properties. The clusters are primarily young (~108yr) and massive (~104.5M_{sun}_), with median half-light radius 7pc and dissolution times of a few Gyr. The properties of the M31 clusters are comparable to those of clusters of similar age in the Magellanic Clouds. Simulated star clusters are used to derive a conversion from statistical measures of cluster size to half-light radius so that the extragalactic clusters can be compared to young massive clusters in the Milky Way. All three sets of star clusters fall approximately on the same age-size relation. The young M31 clusters are expected to dissolve within a few Gyr and will not survive to become old, globular clusters. However, they do appear to follow the same fundamental plane (FP) relations as old clusters; if confirmed with velocity dispersion measurements, this would be a strong indication that the star cluster FP reflects universal cluster formation conditions.