BERLIN—Daimler AG and BMW AG, two of the world’s biggest manufacturers of high-end vehicles, are expected to unveil plans to expand existing cooperation to include the development of self-driving vehicle technology, a move that underscores how heightened competition is pushing longtime rivals to work more closely together.

The companies are expected to announce they will jointly develop self-driving-vehicle technology for highway driving and self-parking applications, key features that are expected to be high in demand by...