Qualcomm Inc.’s agreement to pay $39 billion for the world’s largest developer of chips for automobiles represents a huge bet on cars becoming the next smartphone—a way to roll together communications and services once handled by dozens of other devices.

San Diego-based Qualcomm isn’t the first tech company to eye the automotive industry for expansion, and the jury is still out on whether the deal will help make cars smarter and safer. But it shows the degree to which interest in turning cars into digital-technology showcases...