Intel Corp. agreed to buy Israeli car-camera pioneer Mobileye NV for $15.3 billion, one of the chip maker’s biggest acquisitions ever and the latest bet on Silicon Valley’s vision of cars as turbocharged computers on wheels.

The deal, which amounts to a 34% premium over Mobileye’s closing share price Friday, would give Intel ownership of a widely used technology in the rapidly emerging business of computer-assisted driving. It also would give Intel a long list of customer relationships Mobileye has with auto makers, including...