The best predictors would appear to be a high math GRE score, being foreign, and having recommendation letters from "quality professors." Here is the paper and data. Those indicators also predict research productivity. Thanks to Craig Newmark for the pointer; here is his source.
Do beware the general problem with this kind of study. It is easy to set up a model where GRE scores do not predict later academic success, precisely because GRE scores are used as a dominant criterion for admission. An admitted student with low scores presumably has some other virtue in his favor. Yet it would be wrong to conclude that scores, in the population pool, are not correlated with quality. The real trick would be to look at a broader pool of applicants, not just those who were accepted and attended.