AbbVie Inc. will pay Boehringer Ingelheim GmbH at least $595 million to join in developing two drugs aimed at treating psoriasis, Crohn’s disease, asthma and other diseases where the immune system goes awry.

Beyond the upfront payment, closely held Boehringer is eligible to receive additional, undisclosed payments tied to developmental and regulatory milestones, as well as royalty payments on sales.