Valeant Pharmaceuticals International Inc. for a year has weathered a scandal over its relationship with a mail-order pharmacy that critics say helped it secure lofty prices for its drugs.

Now prosecutors say they have uncovered another troubling connection between the two companies. They alleged Thursday that two men—one from each company—enriched each other through a multimillion-dollar fraud and kickback scheme by directing more business and money to the pharmacy, Philidor Rx Services LLC.

Valeant...