Jimmy Iovine and Dr. Dre are taking senior positions at Apple

Music mogul Jimmy Iovine gravitates to the limelight in a way that previously might have made him ill-suited to work at Apple Inc., AAPL -0.42% which historically had one face:Steve Jobs. But as Apple completes a deal to buy headphone and streaming-service company Beats Electronics LLC from Mr. Iovine and his co-founder, rap star Dr. Dre, both men are likely to take senior positions with the Cupertino, Calif., tech company, according to people familiar with the matter, commuting from the Los Angeles area to Silicon Valley—or meetings elsewhere—as needed. Though the details of the men’s potential Apple assignments remain unclear, the mere possibility underscores how Apple’s corporate culture has loosened under the leadership of Mr. Jobs’s successor, Chief Executive Tim Cook.