This is an important question, and I think there are two ways to approach it. The first is that, as someone in a leadership position, you have to demonstrate that reading is important to you; you show how valuable a behavior is by participating in it yourself.
That said, while you can require that designers read, you can’t force them to care. The better method is to hire designers who care about reading in the first place. Based on the warm responses I’ve received from this article, it seems there are quite a few of them out there.
After nearly a decade in the publishing business, I’ve developed a habit of asking prospective hires what book they read most recently. There’s no reason this question can’t be asked of designers as well as editors or writers. If they answer with a book you also find interesting—or which they convince you is interesting—then you’re on the right track; if they answer _with three or more books_ that you find interesting, then it’s likely you’ve found who you’re looking for.