Apple Inc. has tapped a highly regarded senior executive who helped bring to market many of Apple’s signature products to oversee its fledgling automobile project, according to people familiar with the matter.

Bob Mansfield had stepped back from a day-to-day role at the company a few years ago, after leading the hardware engineering development of products including the MacBook Air laptop computer, the iMac desktop computer, and the iPad tablet. Apple now has Mr. Mansfield running the company’s secret autonomous, electric-vehicle...